Heya!
CC/SoE are one big server, for all intents and purposes. I think they’re both on West coast time. The only thing to watch for is making sure you have the correct “Name-Server” when mailing stuff. 
The RP is still very much active here! It is mostly centered around guilds and events, though walk-up is still a thing, especially if you notice someone with an RP profile, like TRP3. That said, the walk up is not on the scale of a larger server like WrA- but it does occur, and once you know where to look, or find a group of people you like hanging out with, RP is pretty easy to find.
For a list of current events, check here:
There are several weekly events, and each faction has an OOC channel for helping people get into the servers’ RP:
-AllianceOOC and
-HordeOOC
You can jump in there and ask about events, or guilds, or just see if anyone is hanging out somewhere RPing!
I believe (but don’t quote me) that the servers lean a tab more towards Alliance in terms of population, overall, but I play on both factions and the RP seems pretty even. There may just be more Alliance players overall. Or it may be that I have slightly-more Alliance alts than Horde alts. But, you’ll find RP on either side- or both! 