It includes my sister's, which starts going be-be-be-beep every five seconds, and after 30 seconds gets to be-be-be-beep, and eventually works its way up to be-be-be-beep, by which time you are expected to be awake.

I dunno; mine starts with BEEP BEEP BEEP ... and it sometimes takes me 3 minutes to notice it's going off. I don't think a progressive one would help me in general, and I'm quite certain a quiet one like that wouldn't.

Notably, the linked article on sleep inertia suggests other (including less healthy) methods of dealing with sleep inertia: noise, activity, and (of course) caffeine.