When I first started roll hunting, I didn't have any accounts with the local banks. I tried buying boxes from three different branches. The first two didn't ask if I had an account. The third did ask. Like everyone says, it varies.
You asked for alternatives, and there is one that I can think of: Go to a bank that has a coin machine and ask to buy bags of coin. One of the local banks here has a coin machine and told me that they will gladly sell bagged coins to non-members. It is a win-win for them. They don't have to deal with it taking space in the vault until the pickup, and they won't have to pay any additional fees to their carrier for counting (if applicable).
I know the bags of pennies are $50, and I'm pretty sure the bags of halves are $1000.
The other thing I'd suggest is that you tell them your circumstances. Tell them that you are a Canadian just down there for the weekend, and that you collect U.S. coins, to which you have limited access in Canada. That will let them know that it is a one time thing, and that they will never see the coins again. I think the teller would be far more likely to help you out.
Also, as suggested above, if you only want a few rolls, I doubt anyone is going to ask. They'll just grab them from their tray and give them to you.