Sure, you can but I don't presonally recommend it. Reasons:
1) You'll have to install some type of 'sheathing' or flat material (like 1/2" insulation board) first, right on top of the shingles, so the vinyl lays flat. This is not only recommended by the Vinyl Mfgr. but required if you don't want to void the warranty. If you're gonna go through all this trouble, you might as well remove the shingles, (since it's most likely smooth underneath that), then (if you like/want/have to), put up the insulation board (or whatever), THEN install the vinyl. Besides, with all the banging that's going on if you're doing this over top of the shingles, you're bound to break an awful lot of them anyways (thus causing uneveness.) Believe me, you and anyone including a prospective buyer will notice the 'imperfections'.
2) These days, with a 'thing' called Seller Disclosure, if you go to sell your home and you do as you are asking, you'll have to disclose the asbestos shingles under the vinyl. Most folks 'freak out' when they hear there's asbestos in, or ON, the house. I know it's non-friable, and probably so do you (which makes it fairly safe to handle). BUT, 'they' don't necessarily know that.
3) Over time, the shingles behind the vinyl start to fall and such. It may take only 1 shingle to 'cause' a 'bulge' in the vinyl. Once that starts to happen, it doesn't stop. Remember, all that hammering of the sheathing/insulation that's used to cover up the shingles will loosen them up. And on top of that, the wind will 'rock' your house and loosen the shingles too. It just gets ugly.
I'm sure 'others' will have their opinion on this but I will say that the removal and disposal is not that expensive. Read my Follow-ups in this post: Asbestos Shingles (do read them both.) In the second follow-up, I talk about the disposal of the shingles.
If you have more ?'s, ask away. My best to ya and hope this helps.
Jay J -Moderator
PS: Others may disagree but that' OK w/me. You'll just have to decide for yourself based on the info you read ...