The ride quality won't be perfect (but you'll never notice it on gravel) but l would definitely patch both the tube and the tire. You know how to patch a tube.

For the tire, in most cases, l found that cleaning the inside of the tire carefully (with rubbing alcohol) just a few inches around the hole and then making an internal tire patch by sticking 4 to 6 or more layers of duct tape (switching directions so the fibers run 90 deg in opposition to one another) makes a pretty tough and fairly durable patch. The tire patch only needs to be about 1 to 1.5 inches in diameter for most tire cuts.

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You can also use tubeless tape (perhaps in conjunction with gaffa) as that's more or less made to not let a tube squirm through a hole.