Not really. It doesn't rely on that big of an assumption, nor does it require nation state resources[0]. When you're trying to find the secret you can make a bunch of requests and measure for statistically significant change, which can still be detectable beyond jitter & web server load.
Also ignoring the fact that calling constant_strcompare(string, string) instead of strcompare(string, string) when working with secrets isn't that big of an ask.
If you could measure the time granularly as a client requesting some resource on the server how exactly would you know the time corresponds to the comparison and not to some tangential task?
Also ignoring the fact that calling constant_strcompare(string, string) instead of strcompare(string, string) when working with secrets isn't that big of an ask.
[0] https://crypto.stanford.edu/~dabo/papers/ssl-timing.pdf