Yes, setting $| on a filehandle disables buffering. If you do that to produce dots as you go, I guess you're taking a penalty of a few nanoseconds per dot. Considering establishing a connection and pulling a page over HTTP will take anywhere from a few milliseconds to several seconds, I don't see why you should even care about about your prints.
Performance should be your very last concern, and only if you have found that your code is actually too slow in practice. Even then, you don't start guessing at what could be made faster: you profile the code and look at where it's actually spending its time. If a script takes 3 minutes to run and you accelerate a random part of the code by 10 times, it doesn't help you much if that part of the code only took 1 second total of the runtime anyway. You're now down from 3:00 minutes to 2:59.1 minutes.
The network I/O is going to take so much more time in your script than anything else it does that no optimization is going to matter. If you want it to go faster, make your downloads go faster. If you can't do that, don't bother changing anything.
Makeshifts last the longest.
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