It can be done if you're so motivated. You can patch the inside of the tire with a regular inner tube patch, and you can use a needle and thread to stitch the cut shut. If you're going to repair the tire, I'd suggest doing both. Note, however, that it's better to be sentimentally attached to the idea of tires and tube remaining inflated and intact rather than to a tire itself. The former increases the odds that you won't end up on the ground as the result of an inopportune flat.