HI Gang,
Tried that myself a long time ago. An article in Handloader told how to make a thing called a "Wilkes check".
It used a couple of gas checks cast into the band grooves in the mould. They had holes punched thru the middle of them. I made some & they didn't seem to work all as good as we thought they might. Used a Lyman 311291 mould. A good way to use up spare gas checks is about all.

Just starting to think of doing my own casts; I've read that the traditional way is to seat/crimp the gas check after the bullet is cast, during the sizing process.

Are there moulds wherein the gas-check is cast along with the alloy?

I don't think that anyone does now days. Years ago saeco made copper base bands you put in one of their moulds and poured into them. SLW

The time that it would take to fit a gc in a mold would cool the mold to such a state that you wouldn't get a good fill out of the mold. Cast hot, cast fast, and fit the checks after you sort your bullets.

I'm currently playing with some jig molds for fishing, and fitting anything in a hot mold, ie gas check, fish hook or line eye is a royal PITA.

Art, I played with that a long time ago. I made a special punch that would cut a hole in a gas check. It could be placed anywhere in the mold, front, center or rear drive band. It worked OK except for the trouble of setting it in place. Running them through a size die makes them fit so the mold blocks will close.