Yes, at least the Docker images that use glibc as their libc. (eg, most Debian/Ubuntu images)
It looks like musl, which is used on Alpine Linux images for example, will only read it once, and then cache it:
https://github.com/esmil/musl/blob/master/src/time/__tz.c#L1...
It has a mutex/lock around the use of the TZ info, but avoids re-stat'ing the localtime file.