Do we have a thumb sucker?

Like most babies, Bridget has really taken a liking to her thumb, though she still loves seeing if she can fit both fists into her mouth at one time. I'm not encouraging the thumb sucking per se, but I am CERTAINLY not discouraging it. Many times it's helped her stay asleep longer, and it has definitely stalled some meltdowns. And besides that, I think it's cute! The only problem with it for now is that when I put her on her tummy for "tummy time," she loves sucking on her hands more than keeping her head up to strengthen her neck muscles. So, if anyone has any great advice on how to improve tummy time, please advise! She hates being on her tummy so tummy time rarely lasts more than four or five minutes. I've even bribed her with the t.v....haaa, haaa, haa...I'm such a good mom!....But she is fascinated with the t.v. (we don't let her watch it, but when she sees it is on she is totally mesmerized by it), so I decided to see if that would motivate her keep her head up. It's helped for a minute or two, but that's it....so advice is welcome!