How feasible/reliable is welding a pre-drilled gas port closed? Key thing is this would be in a big bore AR application, so Max psi would be around 40,000.
Gas ports are easier. We weld/repair gas ports all the time.
In your OP I assumed you were referring to a hole larger than a gas port, like in the .100-140" range typical of scope base screw holes, not the .065 - .095" size typical for gas ports. A screwed in plug is better for larger holes while gas ports are far more forgiving of shortcut repairs (or as I call them, cost-effective).
[For others, see the comments in the OP for the original reply, here]
It takes very little to close up gas ports with TIG and the tiny recess left in the bore doesn't affect ballistics in any practical way that I'm aware of. I would not be concerned with bore pressure and the repair. It takes a LOT to breach solid metal, although I would spend a lot more time and care on a chamber than a barrel bore (and yes, we've repaired chambers--see below). Having said that, I have never seen a bore/chamber repair fail under pressure. Fail by my quality standards, yes. Catastrophic failure, no.
If you've ever tried to remove a press-fit front sight post cross pin you know that even a taper fit pin is pretty solid. I wouldn't try that on a bore repair but my point is that the gas pressure isn't that big a deal for this purpose.
For gas ports (i.e., small holes), we use a carbide spot drill to make a 45 degree x 0.100-150" depression for the weld (a center drill will work too). Without the depression for the weld, it takes too much heat to get a good weld puddle and that makes for a lot of finish work to recontour the barrel. You also can't tell how much penetration you got since the puddle wants to spread horizontally rather than get into the hole itself. By puddling the rod into the depression you made you know you got down at least that deep and have a good, reliable, solid repair.
We don't use a plug per se, just a short piece of TIG rod that falls short of the bore and sticks out about 1/2" above the surface. It's then puddled into the chamfer and slightly proud of the surface (for hand finishing). Solid core MIG wire works too but we use .030-045 wire which is too small for a tight fit in most ports. A set of pin gauges helps here.
Wish I had a couple of pics...easier than describing it, LOL.
We use TIG rod because it's convenient and soft enough that in the unlikely event it does end up protruding into the bore, it can be easily snapped off with a length of hardened drill rod sharpened at a 30 degree angle (like a sharp, flat, one-edged chisel point). One tap with a hammer and the TIG rod shears easily. And that's only happened a couple of times in 40+ years.
FYI you can get precision ground drill rod from McMaster-Carr, etc. if you ever need to make caliber-specific ranging rods (or to make a chisel to get rid of a botched plug). We have a set on hand to verify bore clearance for muzzle devices or suppressors where the coaxial alignment is questionable (it's happened). Cheaper than baffle strikes. Making your own is pretty easy and FAR cheaper than a set from Brownell's or Clark.
Since I mentioned it, chamber repairs require greater precision, rough and finishing reamers, and much better finishing/polishing technique. Depending on the extent of the chamber repair, we often take the opportunity to set back the barrel by one thread to get the best possible repair and a nice smooth, verified good chamber surface. A rough chamber guarantees an angry customer. Chamber repairs are a lot of work ($$$) so unless it's a really good barrel (like an F-Class, antique, or rare) fitting a new or good used barrel is usually more cost effective.
Hope that helps with your particular project.