Not specifically address space layout randomization in the way it's usually implemented; ASLR as applied in most modern production OSes randomizes each stack's base address, but each stack is still laid out and used in a normal way. There are some research projects towards actual stack layout randomization (involving stack rearrangement via static analysis, randomly sized stack padding frames, and other techniques) which would also definitely blow up cache, but none that are mainstream in a production system as far as I know.

However, for the naive case where the recursion is a full-blown function call, without some kind of optimization, other security mitigations than ASLR will significantly affect the efficiency of recursion by adding function call overhead (and possible cache side effects) - for example, the stack cookie will still be verified and control-flow guard checks and the shadow/return stack will still be in play, if present.