Yes, it does save memory and bandwidth... I also ran a speed test (which is not completely germane to this question, but is useful and suggests that it does stop reading the stream) and a memory test just to demonstrate. I did not run a peak memory test, but at the very least your $html variable will store less information and save memory there.
Time to get ALL characters of remote page 10 times: 6.0368211269379
Time to get ALL characters of remote page 10 times: 6.0158920288086
Time to get ALL characters of remote page 10 times: 5.8945140838623
Time to get ALL characters of remote page 10 times: 8.867082118988
Time to get ALL characters of remote page 10 times: 5.7686760425568
Time to get first ten characters of page 10 times: 4.2118229866028
Time to get first ten characters of page 10 times: 4.5816869735718
Time to get first ten characters of page 10 times: 4.2146580219269
Time to get first ten characters of page 10 times: 4.1949119567871
Time to get first ten characters of page 10 times: 4.1788749694824
Memory Useage First 10 characters:40048
Memory Useage ALL characters:101064