Can I put a t-shirt in the post office mail box without going inside using ReadyPost Utility Mailers?

Yes, you must go inside - unless you are using a "Prepaid Express Delivery" envelop - You won't be asked to buy a bunch of stamps - the clerk will look at where you are sending it to, and determine how much the postage will be, and make up a stamp to place on the envelop. Be sure that every edge is secured with tape - you don't want it to open on the way to the addressee.