Unfortunately, I'm stuck with whatever build of Perl the operations staff compiles. We're currently on v5.10, which does have thread support built in, but if a future release comes along that omits it by default, I may be out of luck.

Version 5.10 is more than 8 years old. If your ops team keep on this path you'll have a good 8 years to plan your migration away from threads in the unlikely event that it is removed from perl.

[perldoc] states that discouraged features are considered to be "mistakes" that may one day be deprecated.

That is true. However, there would be a serious outcry if threads were removed from Perl5, given the amount of code which requires it. And deprecated != removed, so even in a worst-case scenario you'll have plenty of warning.