If the user is expecting to access all their notifications going back to the first day they signed up to your product, you should provide that for them. This has some backend implications in terms of how much data you want to store vs at what point is it sensible to delete old notifications, etc.
As a listing of notifications, how many notifications the user has in the list is not a problem. The problem is how the user can navigate through them.
I think Gabriel's infinite scrolling solution could work but only in conjunction with a date filter / timeline.
Imagine accessing notifications from 2 years back. Only using infinite scrolling would require the user to scroll through 2 years of notifications to see those old ones. Check how Facebook handles their notifications and Timeline. It is a lot of scrolling.
Implementing some sort of timeline or date filter will allow the user to first navigate to the year/month/date and then search for the notification. You could activate infinite scroll at the year and month level, but load all the notifications if the user specifies a date.