Not in normal gameplay. I have a void base that has vertical connectors from surface to -3k, and an above water tube from north of the gun island to the void base. Several mini bases scattered around, a big aquarium build in the jelly caves, and a cyclops accessable storage center in safe shallows (lots of storage lockers)

The only base that actually lags is the void base, adding or removing structures takes a second, and the tube, even though split up to only take me down 1k at a time lags extremely when looking at the ladders. The hologram when planning to build can also cause extreme lag. However when I'm just in the base, game runs fine, max fps only drops from 123 to 115 on max settings, so fps cap on makes that unnoticed. For the smaller bases there's some slight fps drops when looking through a series of windows (maybe? Could easily be some unknown factor)

When just out in the world there's no effects, as they aren't loaded, atleast completely to my knowledge.

There used to be a bug that would make big/multiple bases a bad idea, but it seems much more tolerable now, unless you're an idiot who builds a void base, in which case i can't really be suprised on the fps loss.