I wouldn't. First, it's never safe to click on unsolicited links. The ones you actually sign up for are bad enough. Second, who cares about a weekly Youtube update? If you are really interested, wait a week or two and see if they still keep coming in. You've lived this long without youtube updates, you can wait a couple more weeks. If it's legit they'll keep sending them. If it's phishing, it's probably a one time thing.
Edit: I just did a quick search, and it appears Youtube does offer weekly updates. But I still wouldn't click on the link. I'd sign onto my Youtube account directly and either unsubscribe or manage the feature to make sure it's legit. I'd still be suspicious based on this being the first one. Unless, of course, you just created your account in the last week or so.
"Good judgment comes from experience. Experience comes from bad judgement." - Will Rogers
DW and I - FIREd at 50 (7/06), living off assets