You could, as the nail is close to the center of the tread, where the tire carcass is most stable. That said, I wouldn't, personally. With so much riding on so little, I've never felt it was worth the risk. But, so long as you have an internal plug/patch applied (and properly), you'll probably be ok.
I had it patched from the inside and since nail was small and barely went in, also on the angle as you see on the video.
I didn't want to enlarge the puncture and use one of those plug/patch "mushroom looking patches" and went with just straight flat patch.....well guess what?
It still didn't work!!!! Think I'm done messing with it and wasting time, gotta get a new tire.
Now question is....? I got 5k miles on the bike, both front and back were in good shape.
Do I just replace the rear? Should I stick to (think its MPR3), Would it be OK to get different brand?
Really don't want to spend that much but should I buy two new tires?
That's exactly why those mushroom patches are the only workable option! The plug part seals the hole, while the patch part seals the inside of the tire. It's the ONLY acceptable type of tire repair on a bike!!
As for replacing the tire, I'd recommend sticking with a stock replacement for now. You don't want to end up on a set of tires where, say, the front is a quick steering, triangulated shaped tire, and the rear is a wide, slower steering shape. Having comparable traction, steering traits, and shape and height of the tire is important to keeping the bike predictable.