For the most part it will, but the values of the TypeOfLevel parameter in the level header were changed around, which means that you'll have to change that value to play the map in the correct gametype (which takes like five seconds, so no biggie).
And as for SOCs, SOCs always break with each update that adds new Objects to SRB2, because they overwrite slots that were previously unoccupied. This happened when 2.0.5 came out, it happened when 2.0 came out, it happened when 1.09.4 came out, and so forth. Sometimes you're lucky and the SOC in question doesn't use any of those newly occupied slots - in that case the SOC will still work. But lots of SOCs use the first free slots that are available, and since those are the first to be overwritten by new Objects, those SOCs will break.
Now there's one silver lining, so to speak: 2.1 will be the last time you have to update your SOCs. That's because 2.1 introduces a new feature where you don't have to specify the slot numbers yourself anymore - you just write down a name for the Object and the game will automatically find the next unoccupied slot and put it there. So when a potential 2.2 comes out and adds new Objects, this will no longer affect SOCs for 2.1, because the game will automatically shift the slots around for you. A great side effect is that this prevents conflicts between SOCs. Right now, if two SOCs use the same slots and you add both, they won't work correctly because one overwrites the other. This is why you weird things happen sometimes when you load two separate level packs, like Tortured Planet and Mystic Realm (although I think those two have no overlaps - just an example off the top of my head). Starting with 2.1, the game will automatically prevent any overlaps, so you can add as many SOCs as you want (at least until all slots are occupied) and there will never be any conflicts. But, as I said, you will have to do this one last update to 2.1.
As for character WADs, I don't know if they changed anything about the OBJCTCFG, but if they did, those will have to be updated too (and since they removed a lot of restrictions, you might as well update them even if no changes are necessary). Unlike the 1.09.4/2.0 transition, you won't need to convert the sprites though.