Nope. But they have a coupon page where you can clip diaper and wipes coupons electronically. I think they have four right now. I have the page bookmarked. Click here.(They are under health and personal care)
ETA: Click "see all" otherwise you only scroll through part of the coupons.
Amazon doesn't, but diapers.com will accept manufacturers coupons, see here. I always order through Amazon though, so I'm not sure how their prices compare.
I wouldn't stock up right now since you don't know what will work for your baby. You might buy a ton of Huggies and find out that they leak every time and you need Pampers or one brand gives your baby a rash. Then you'd have to go through the hassle of trying to exchange the
unopened packages through whatever online retailer you used. I wouldn't start with a huge package either. If
you try them for the first time and they don't work you don't want to have an opened box of
200+ diapers you can't use or return.