Web check-in isn't just about getting through security. It's also a powerful tool when positioning yourself in the upgrade queue.

Once you check-in that time sorts you within your elite category -- so using web check-in even without a printer has value to the flier without a confirmed upgrade.

If you don't have a printed BP that's ok -- just walk up to the ticket counter (or a kiosk) and check-in normally. They'll "re"-issue a BP to you. Occasionally they do a double take when they see that you've already checked in but the process is no different then losing your BP between flights or something. It does not, for instance, reset your official check-in time. You just get a new piece of paper.