Monitor as in "see what are people watching" - absolutely not.
Monitor as in "see how much data is going to/from youtube" - also not really:
At the moment, there is no way to reliably detect all youtube traffic by content of packet. You can block youtube by blocking youtube IP addresses (and instead of IP you can use hostname which will be automatically resolved by DNS to all currently available IP addresses). that will block clients from accessing youtube user interface, therefore users will be unable to play any video.
However, if you want just monitoring, not blocking, you must monitor both user interface and video delivery. Unfortunately, for video delivery youtube use "*.googlevideo.com" (for example https://r5---sn-uxanug5-hxay.googlevideo.com
) which can't be added to address lists because wildcards cant be resolved to IP (infinite amount of combinations in wildcard). You would have to speficy each domain/ip address which youtube use and thats not really possible. You will either not pick up all addresses or you will pick more than just youtube. Therefore it is unreliable - any results will not correspond with reality and there is no way to say how big the error is. It can be few percents, it can be hundreds or thousands of percents