First of all, the wheel offset is almost always cast into the backside of the wheel. Pull a wheel and inspect.
Second, Having acquired an F150 in the last couple of years, I get a chuckle out of the whole "will it rub" questions. Its a legitimate question, don't get me wrong, but the problem is the question is so subjective. If you drive like a grandma and use your truck to fetch groceries and take the kids to soccer practice, then you could probably run some 37's and maybe rub occasionally, if you drive the truck like you stole it on the dunes or some backwoods trails you will have problems with 33's. OK, so maybe 37's is stretching it a bit, but ask me how I know about the issues with 33's.
Here is what I can tell you. Your full compression will be limited by the tire hitting the top of the fender lip. Get you some bump stops, cut your fender opening or get you some different fenders. Will you push the truck to this extreme? Most do not, that is for you to decide. You will also experience some rubbing at some point if you do nothing. Can you live with the rubbing? Sure you can. Do you want to live with the rubbing? That is for you to decide. Are there solutions to fix the rubbing? Yes, start trimming and cutting, or pick you up some large opening fenders (ie. Glassworks Unlimited)