YES!
But wait... It greatly depends on the particular video you're listening to, whether or not the person who uploaded the video has a decent mic and is relatively close to the speaker.
If done decently, though, you will
absolutely be able to discern the tonality of the speaker.
You should be using a good headphone. I'm using the Sennheiser HD650. You will need to compare the recorded song over the speaker to the original file in order to truly know whether or not the speaker is introducing any coloration.
The song being played in the
video is "Autumn Leaves" which is this one.
When I compare the original song file to the Tannoy 12 DMT II, I hear a shouty/honk coloration that is not in the original song file. That speaker is introducing coloration which may or may not sound pleasant to your ears. I do not find that type or coloration pleasant and wouldn't purchase the speaker.
Here's another video demonstration which is done the right way. It's in Chinese, but you'll easily be able to figure out what's happening.
Put on a good set of headphones, and
most importantly click "
See More" under the video title to expand the list of songs used in the video. Open those song links in another tab to compare the original song to the speakers playback, one by one. When doing so, I was easily able to discern that the Genelec 8351B was the best in the bunch of those compared. I could not detect any added coloration and the mic recording sounded nearly identical to the source files. Not surprising, since this speaker has utmost praise both objectively and subjectively.