In general, yes

In nitpicky detail, I’d prefer it to not clear when you log out – that would lead to annoyance when I need to leave for whatever reason when I’m halfway through checking the list of updates.

I’d prefer a “Mark as read” system to handle removing stuff from the recent update view, that way I can log on, check the updates list and read a couple of things, get interrupted and come back later without missing anything, then at such time that I’ve caught up with the updates I can mark the rest of them as read.