Definitely no issue checking cardboard boxes. Have done it many times. You may want to create a handle using a strap, string, tape, etc to make it easier to carry. Sometimes I even put frozen food with ice packs in them. Just make sure its packed well. Make sure it will hold up to being dropped a few feet.

In fact, I often see them loading USPS mail and their packing is much worse. Trays of letters with flimsy tops where they would fall out if you just shook it a little and what looks like clear plastic trash bags.