That shouldn't reduce performance too much, right? Getting the current time is such a frequently-executed system call that, as far as I understand, its implementation is in a vDSO in Linux that is loaded into every process. This means you shouldn't need the full cost of a system call when you get the current time.
Nice to see someone else thinks about this.
In my personal project webserver I don't. I didn't measure, but just trying not to do unnecessary work.