Yes, patching a tube when the hole faces the rim is easily doable. But you obviously have to do a good job patching to avoid having that particular hole leak again.

BUT, that said ...

Even if you do a great patching job, you must try to figure out what caused the hole. Because, since the hole faces the rim, if there is something sharp in your wheel that caused the first hole, without truly solving the issue, the thing that caused the initial hole will repeatedly cause more holes, and more flats.

Does that make sense?

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Check the rim strip.

I've had a misaligned rim strip result in the tube bearing against the edge of a spoke recess with the result that the tube ruptured almost immediately.

Checked everything and even rode on it. Nothing. Which lends me to think it was either my half assed tire wrenching or my cat got a poke when I wasn’t paying attention.

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I still lapped everyone on the couch!

Are you using rim tape like velox or Stan’s or a plastic rim strip? I’ve found the rim strips to move around quite a bit during installation of tire and tube. Once you have the tire and tube installed, no air, recheck that the strip is still centered and even on both sides. If these are the same tubes and rims as before, that worked fine, and the failure is on the rim side, it must be the installation. Also, try a new tube, patches can be tricky. One more bit of advice, and I’m only mentioning this because of the failure spot near the valve, always insert tire levers on the opposite side of the valve, you’ll get a little more room.