I hope so!
Well, the wrapper should not affect the cache, but I guess you did not mean updating the wrapper (the jar checked into VCS) but the Gradle version the wrapper uses to run your build, defined in the wrapper properties.
A different Gradle version could behave differently and produce a different result, like a fixed implementation of some logic. The Gradle jars should be part of the classpath of the task and the classpath should be part of the cache key. So if that minor Gradle update does not change the classpath, the cache key might be the same, but I'd say that's rather unlikely.
But simply enable cache debugging, then you see exactly how and from what information the cache key is built, then you can compare.