The general answer is no, with a couple exceptions.
Keep in mind that with most GA flying the pilot actually knows the passengers. Even before 9/11, if I didn’t trust you or thought you might pose a hazard in the air I just wouldn’t invite you to come into my airplane. If I am so suspicious of you that I’d want you to be searched and patted down prior to boarding my airplane I just won’t take you along. It’s not at all like commercial flights where you’re packed into a tube with random strangers who may or may not be good people.
If it’s a corporate jet, well, it’s owned by the company and I’ve yet to see such a situation where employees were allowed willy-nilly to commandeer the company jet because they are Very Expensive even just to start the motor, so who had access/authority to use the company airplane was pretty tightly controlled. Where I used to work in corporate America the company didn’t own a jet but used charter. The charter service did want to know who was boarding the airplane and asked for identification to make sure they had the correct people on board (wouldn’t want to mix up two groups of executives, right?) and reserved the right to make further inquiries, but because most of the people using the service were repeat customers, often to the point the charter company staff would recognize them on sight or their voices over the phone, repeated TSA-style searches would have been a bit ridiculous, wouldn’t it? Luggage might generate inquiries, and that’s always been the case, because of concerns about weight and balance in small airplanes and also some things that are safe on the ground might cause problems when airborne. Charter services have the authority to search your luggage, but they may choose not to do so.
In other words, non-commercial GA generally isn’t flying complete strangers around. Commercial GA might, but there are usually other layers of access control already in effect, and while they don’t have to, they certainly have the authority to ask for a search or even to refuse service if they have a reason to be suspicious. In both cases, passengers are frequently much more of a known quantity to the operator than is the case with the major airlines. Requiring everyone to go through TSA-style searches would, it is currently believed, not do much to increase security and cost enormous amounts of money and time. The cost far, far outweighs any imagined benefit.
The exception to this would be GA flights out of commercial hubs. For example, if I were to fly my GA airplane in to Midway, go do business in the city, and come back to my airplane I would have to go through security screening to get back to my airplane. Likewise, passengers boarding a charter plane at such an airport would also have to go through screening. This is because of concerns about a possible security breach between the GA and airline areas at the airport. Another way airports with passenger service handle this issue is by maintaining rigid separation between GA and non-GA areas of the airport. Gary airport in Indiana does this - GA airplanes are not permitted on the areas of the airport used by airlines (when we have airline service - it’s been off and on), nor can a GA pilot simply walk over to that area via the non-public areas of the airport. Indeed, there are wandering security people patrolling that airport and once or twice I have received a knock on a cockpit window or simply been asked my business while there. Perhaps I should add that it’s not unusual for a large airport to have separate areas for GA, airlines, and military operations as well. We may share the same airspace, but that doesn’t mean we’re parking next to each other on the ramp.
As far as parking an airplane and leaving it without apparent guards - there are ways to secure an airplane that make it more difficult to randomly steal it. These are not always obvious from the outside of the airplane. Locking devices are becoming ever more common as well. Granted, that wouldn’t stop a determined team of ninjas from mounting an armed assault on a GA ramp, using tools to defeat anti-theft devices, and hot-wiring the ignition system but then a lone security guard or the unarmed TSA guy inspecting your socks won’t stop that, either.
Bottom line is that security doesn’t have to be squads of uniformed people or even particularly visible to be present. With GA the emphasis has been more on limiting access to equipment rather than minute inspection of the passengers (a lot of GA flights don’t even have passengers, not even one.) Regardless, though, if I as a pilot get on the radio and yell for help, or simply say something looks funny over there, rest assured there will be all sorts of authority figures coming out of the woodwork. That nice lady behind the counter in the office - you know that reception area, the one with all the windows overlooking the field? - has some idea of what’s normal and who should be where and knows how to dial 911 or various other emergency numbers to deal with a situation.