More specifically:
For a commercial airliner, is there some available combination of thrust, forward speed, and angle of attack that will enable it to sustain level flight with the spoilers fully extended? Or do spoilers kill so much lift (and create so much drag) as to make this absolutely impossible?
Surely a real expert will soon chime in, but maybe this is relevant:
There are inflight spoilers and ground spoilers. Inflight spoilers can create rather high descent rates, higher than max climb rates. As a WAG I don’t think a typical jetliner could maintain level flight with full inflight spoiler deployment, although the descent rate would not be horrible.
Deployment of ground spoilers in flight leads to very high descent rates. There have been many accidents due to this. I am quite confident no typical jetliner can fly level with full ground spoilers deployed. E.g. Air Canada Flight 621 (1970)
ETA: climb performance depends heavily on payload. A jetliner might manage to fly, barely, with flight spoilers deployed if it has a very light payload.
I fly bizjets, and I honestly don’t know. In the simulator I’ve done spoiler faults and un-commanded thrust reverser deployments, which usually involve descents and troubleshooting. But level flight? Sure hope I never have to find out.
When you say you train for spoiler faults, does that include deployment of lift dumpers in flight? Is an aircraft controllable at all if they can’t be retracted?
This is the typical, modest remark of a professional pilot. To the rest of this, the correct word would generally have to cover freaking out and trying to repress shrieking terror…
Sustain level flight and then enough control to do anything else, like maybe land? I think the following sums it up:
Note that he said that he’d only ever done the troubleshooting in a simulator. Simulators don’t usually leave most people screaming in panic. If he were ever in need of troubleshooting in a real airplane, it’s possible that he, too, would scream and panic (though of course, the purpose of the simulator training is to make that less likely).
MY only experience is in small aircraft (4 passenger or less) but I recall a warning that with full flaps (about the same thing only… different) that there was maximum speed - you risked damaging the aircraft if they were deployed over a certain speed. I assume the same would be true for spoilers - at least the landing ones. Beyond a certain speed, if modern computers would allow you to deploy, they would be damaged along with associated machinery. SO you would want to try this test at lower speeds - meaning you’ve lost a decent amount of lift due to low speed. So I’m going to guess “no”.
The only large aircraft crash I’ve seen - it was visible halfway across Toronto - was around 1970 when spoilers were applied 50 feet up on a DC-8. It hit the runway, an engine dropped off, and then they attempted a go-round flaming across the sky and crashing into a golf course.
But they do occasionally reduce us to tears. 
Last jet I flew the spoilers could come unlocked (hence, a spoiler “fault”), but I think an actual deployment was highly unlikely because it took hydraulic pressure to bring them out. A TR deployment in flight was also mostly impossible by design - as I recall, the manufacturer wasn’t even required to validate it in test flights, but we did have a memory item for it.
My current plane has a lift dump feature that is manually commanded, so not really an issue we worry about.
The spoilers inhibit movement but don’t decrease power.
If the plane has enough power and the air is thick enough for the plane to hover, perfectly vertical, then the answer will be yes. Hovering in place will be completely unaffected by the spoilers. (Or, if anything, they might help as a sort of brake against going backwards.)
Whether a human pilot could convert any excess power to accomplish that maneuver into something like “level flight”, I couldn’t say but a computer could, presumably.
I don’t know if any commercial airlines have planes that can hover.
Sock alert! (kidding — see post #2)
A plane that could just hover wouldn’t be controllable, unless it also had ‘puffer’ type attitude controls like VSTOL a/c have; otherwise controlling the a/c’s attitude requires air moving over conventional control surfaces, so positive vertical speed. Which some fighters can do, fly at a controllable speed straight up, with no direct reliance on lift from their wings. Even fighters which have had static thrust/weight ratio less than 1 have in some cases been able to do this, fly straight up, at the higher thrust they achieve at higher speed (for example there’s a photo of a pair of F-4’s doing this, although their static thrust/weight at combat weight was only in the 0.8 ballpark). Various later generation fighters have static thrust/weight ratio’s >1, full afterburner at combat weight.
Airliner static thrust/weight ratio’s are usually in the 0.25-3 ballpark depending on a/c, at normal takeoff weights (closer to 0.5 at empty weight plus a little fuel, but still not close to 1).
If you can lift half your weight on your own, how fast do you need to fly to support the other half?
I fly the Airbus A320/321. I don’t know the answer but my gut feeling is that it would do it ok. Spoilers are most useful at high speed, in fact at low speeds (~220 knots or less) they are pretty useless. Putting the landing gear down is a much more effective “brake” than spoilers at those speeds and the plane will happily fly around with the gear down.
Spoilers can be used at any speed.
At high altitude there is only a small speed window between too slow and too fast. There is also very little excess thrust so you wouldn’t be able to do it up there, but at low altitude you have oodles of thrust and plenty of speed margin.
If spoilers could cause big problems, I hope planes display some sort of warning before deploying them. Don’t tell me if they don’t; I’d rather be surprised!
Using them is a normal procedure. In the Airbus there is a warning if you have them deployed against engine thrust, but that is because it’s wasting fuel. There will also be warnings if they have a fault of some sort, loss of power, not in the selected position, etc.
I think that Space Vegetable was envisioning a plane with its wings emblazoned with statements about Rosebud, Dumbledore’s fate, and the familial relationships of Star Wars characters.
That’s certainly what comes to my mind, every time I see this thread.