I don't think this should be a problem...

I am considering a new wheelset purchase. If I make the purchase, I'd probably just buy another cassette, so when I swap wheels, I don't have to take the cassette off every time. But with my new set, I am considering a different cassette config. My current 11-speed cassette is an 11-25, and my new one would be an 11-28. My crank is a compact 50/34. Can I run that on the same length chain? I believe it's 106 links, but I'd have to double check. I would never run a 50x28, usually the biggest combo I run is a 50x19, maybe 50x21. Really the only difference in how I'd use the gears is just having a 28t granny as opposed to a 25t, for the 34 ring. I've never done this before, so I'm not 100% sure how fickle a chain length-gearing setup is. Chain length is determined by the largest number of teeth in combination, correct?

Correct.
Accidents DO happen, so you want your chain sized to handle the BIG:28T.
It'll work perfectly fine on any smaller "large" cogs.

You may find you'll have to turn the RDER barrel adjuster a little bit when swapping wheel sets.
just keep track of how much and it's simple.

I didn't think of that, adjusting the RD, but that's more than likely true. The rim width would be the same, so no brake adjustment (so long as the brake track lines up the same!), but I didn't think of the RD. Hopefully it would be a simple matter like you say so each time I swap wheels the shifting remains clean.

Ideally you want a longer chain to match the larger cog. Also you will need to adjust the B screw on the derailleur to clear the 28T. Barrel adjuster tweaks will depend on on how closely you can match chainline on the 2 cassettes. I run 2 different brand of wheels with a 12-27 and 11-28 cassette on my cross bike and don't need to do any adjustments because the spacing is the same so I don't touch the cable and I just leave the B screw set to the 28T.

You will want to check your low limit setting when you swap wheels so that you do not risk putting the derailleur into the spokes. You are likely to need to make minor adjustments when swapping parts, even like for like, due to manufacturing and assemble tolerances. You may also need to touch up the "B" screw adjustment for best shifting performance. Only minor adjustments should be needed but they will probably be needed to some extent.

I swap out wheels among several bikes frequently. I find I don't have to do very much in the way of adjustments, but I always run through the gears to make sure they won't shift into the spokes. I need to make slight adjustments frequently. Good point, dsbrantjr!

If you size the chain for 50:28t and adjust the derailuer B-screw for that cassette you'll probably get good shifting on the other cassette with no issues. I swap between two wheelsets, and it doesn't require any adjusting. The do sell cassette shims for fine tuning, if it doesn't work right out of the box.

The main issue is the rim external width needs to match fairly closely (<1mm) or you're going to need to adjust the brakes every swap. My rims have ~2mm differences, and the brakes are useless on the narrow rims. Its a trainer, so I just ignore it, but certainly wouldn't work for real riding.