Yes, an adult may use this as a shower gel. It's a detergent, which means it cleans, the product has no way of knowing whether it's being used on baby skin or adult skin. It's just formulated to be milder for baby's more sensitive skin.
Most soaps or washes don't kill germs, they just help get them off your skin so they can be rinsed down the drain. The Gerber Baby Wash will do as effective a job at cleaning and getting rid of germs and odors as any other body wash. Those body washes and soaps that have Triclosan (or some other germ-killing agent) in them actually kill germs, and if the Gerber Baby Wash doesn't have any of that, it won't actually kill any germs, but that's not necessary for proper hygiene, most body washes don't have any germ-killing agents.
You may have to use more of it than you use for your daughter, but you've got more skin, so that's a given. Different people use different amounts for individual best results.
I buy kid's shampoos, body washes, bubble bath, etc., since I love some of the scents they have, and you can't find adult products scented like that, most of the time. Grape, for instance, is really uncommon in adult body washes. I think Aussie Sprunch Spray has a grape based fragrance, but I'm not sure, I just wish they'd bottle that scent and/or put it in a body wash.
And who can blame you for liking a scent and wanting to use it? If you had a friend who found a new perfume you liked, and you wanted to smell that way, too, would it be wrong? No. So why would it be wrong to want to smell like your daughter's scent? I say go for it!