I did a plug in about that same spot (maybe a little further in) on one my tires a couple years ago. Most on here would insist I'm committing suicide, but it's still holding air and the plug hasn't moved a bit. With decent 19" tires at $230 a piece, I'm gonna take my chances. I don't like mixing tires or tread depths, or spending $1000 on a new set when there's 50%+ life remaining. I don't like plugging in that area either, but pick your poison. I closely monitored it for the first couple months, now I give it a look at every tire rotation. Nothing bad has happened in 20K or so.If it was my car, I would drill a hole and plug it at best. I would probably leave it alone however. I doubt plugging it will throw the balance off. I wouldn't go through the trouble of the proper patch plug.
I have plugged several tires over the years without issue. I even plugged a sidewall for my sister-in-law and haven't been sued yet. It's still holding air months later. This is a 215/45/18 Hankook.
View attachment 121640
I've also used the cheap plugs (like you have pictured) anytime I get a repairable flat at least a half dozen times or more (instead of the "proper" plug and patch), and none of them have ever given me any trouble.
To the OP: I definitely wouldn't leave it alone, that would leave the belts open to corrosion and stuff getting into the innards of the tire. I would try the product you mentioned (rubber tire cement or some such product) and monitor it closely for the first couple months / few thousand miles. If all is well, inspect it at least every tire rotation. If you're not comfortable with that, drill it through and do a proper plug/patch for piece of mind, but personally I wouldn't want to damage tire (drill through it) more than it already is.