It depends. If your threat model involved an attacker being able to monitor your power supply (as in some kind of embedded system), they’d be able to see the real work done and separate that from the fake delay.
Except if your 'wait' operation is doing the same computation (add, multiply...) but won't use the result. I often do that in some real-time/low-latency things where you want things constant-time (or can't easily define the worst-case execution time, just make all paths the worst). Then you still need to blind the speculative execution mechanisms so that they don't 'see' you're not using the result.