Am pondering when I kill my next chain, taking the opportunity to do a deep clean on the rest of the drive train (cassette, jockey wheels etc...).
With the cassette (Tiagra 11-34), are there any hidden parts that would be unhappy if left to soak in degreaser (terps?) for an hour?
not really. Turps will make some plastics swell slightly but this isn't likely and is no big deal even if it does happen.
The jockey wheels have bearings in them, so I'm guessing just soaking the whole thing is suboptimal. What's the best way to clean these to prolong the life?
The best thing to do is to remove and dismantle the pulleys, clean and regrease the bushings (basic mechs) or service the ball bearings (some other mechs/pulleys). Immersing the whole rear mech in solvent is a bad idea because the upper and lower knuckles will be stripped of their grease.
Is there any advantage to putting any of these parts through the ultrasonic cleaner?
Not really. Mechs do wear out though; they either wear out in the parallelogram pivots or they wear out at one of the knuckles (usually the upper one). Dirt in either will cause wear. So will stripping out all the lube and not replacing it. To clean the former you can jetwash the mech (careful now) and relube, or repeatedly spray with GT85 and work the mech until what bleeds out of the pivots isn't dirty, then relube (eg using aerosol SFG, wipe away the excess after the solvent has flashed off). To service the knuckles is possible too; you can simply add grease through a spare spring hole in some cases but mostly it requires that you disassemble the knuckles (fiddly and difficult; most folk don't bother). If you are going to do one, do the upper one.
BTW some recent shimano RD designs have a leak path from the parallelogram into the lower knuckle; I have seen one or two where the lower knuckle has seized because of this.
In fairness putting a lot of effort into a RD that is liable to be damaged or wear out anyway (and is cheap enough to replace) is a lot of effort for very little gain. But IME XT and Ultegra level mechs have better pulleys and more durable bushings elsewhere, and these can last long enough that it is worth putting in the effort.
With basic mechs it is usually sufficient to service the pulleys and just remove most of the crud from the rest of the mech, and lube it. By the time it is all a bit worn it is most cost-effective to replace the whole mech.
In an LBS near me 10s mechs are very often going in the bin because they are worn enough they won't work cleanly on 10s systems any more; however the same mechs may still work fine on 7,8,9s systems.
cheers