Is this a theoretical question, or have you seen performance issues? Yes,
it is certainly possible for vacuum to affect the replica performance. More
vacuum activity means more WAL means more WAL replay on the replica, using
up CPU and I/O. In most real-world cases, this will not be a problem, as
the replica should be able to keep up quite well even for near-constant
vacuum activity. You would need a very high WAL volume and a very
underprovisioned replica before seeing any ill effects. There are plenty of
other performance bottlenecks that will likely hit you before this one.
Cheers,
Greg