Ex maritime search radar operator and pilot here.
Our airborne search radar was pretty much limited only by the radar horizon and the time between radar pulses (referred to as pulses per second - PPS) in terms of range for large boats such as bulk carriers, container ships etc. The radar horizon is just the horizon visible to the radar and is limited by the aircraft height and the curvature of the earth. The time between radar pulses limits range because the radar has to listen for a return pulse before it sends the next pulse. therefore the longer the time between pulses, the farther a pulse can travel out and back and still be recognised as a return by the radar. Of the two limitations, the radar horizon was normally most limiting (PPS was automatically adjusted so that it wouldn’t be limiting.)
Radar horizon in nautical miles is given, approximately, by 1.23 * SQRT aircraft height in feet. So for a typical search altitude of 1500’ a range of a bit under 50 NM was achievable for a large boat.
When searching for smaller objects though there are a heap of variations that come in to play.
Things are easier to detect when the sea state is calm, when the aircraft altitude is low with the radar beam radiating closer to parallel with the sea surface, and when the object has ample reflective surfaces, right angles, and is presenting its broadside to the radar beam.
On a calm day we could pick up 10 foot wooden fishing boats with no superstructure or mast, whales, logs, dolphins, fish boils, mooring buoys and other similar bits of crap out to about 30 nautical miles.
On a day with winds above 5-10 knots or so, the smaller items such as logs and buoys would disappear, only large pods of dolphins would show up and whales would only show if they had their tail sticking out of the water. Small wooden boats would be detectable but a lot depends on their aspect. You might still see them out to 30 NM if they are beam on but you might not see them till 15-20 NM if they are bow or stern on to you.
With winds above 15-20 knots finding small things such as low streamlined wooden boats becomes very difficult.
It’s worth noting that when detecting a wooden boat, it’s not so much the wooden surface that is reflecting the radar pulse, but rather the nicely curved surface of water against the hull on the opposite side of the boat. For this reason a traditional boat with a hull that penetrates the water may show up a lot easier than an inflatable raft that sits on top of the water.
My guess for detecting an inflatable raft on a nice day would be at around 15-20 NM. With that in mind I’d set up a search pattern with legs about 25-30 NM apart to allow for some overlap. The aircraft is then effectively covering about 25 NM at any one time and travelling at 200 knots you’d be covering about 5000 square nautical miles an hour. Our aircraft could comfortably fly for 7 hours, call it 5.5 hours of search time allowing for a transit to and from the search area. So, ideally, you might be able to cover 27500 nautical miles of ocean in a single flight.
You can see then that you only need a very approximate starting point in order to know you are able to fly over the appropriate piece of ocean. Unfortunately the chances of actually finding what you are looking for all depends on the weather conditions. If the sea state is up at all then you might have to bring your track spacing right down to a few miles, and even then you might not have any confidence in detection.
Every time I was tasked with finding something specific, it was found within minutes of getting to the search area, but I’ve never been tasked with finding an inflatable raft!
In the case of boats lost in the sourthern ocean it’s quite likely that you couldn’t get a suitable search aircraft to the area anyway.