If a computer player is given an AI (for example, Expansion Protoss Campaign Insane), will it mess with grids by making the computer move the units used in the grid?

It depends on how long the grid is there for. If you're creating/removing the units within 1 trigger, or even in multiple triggers in the same cycle, this is "instant" in terms of game mechanics, and the units will not move. If the mobile grid is created and not moved/removed/acted on or whatever until the next trigger cycle, it's possible that the units could move, likely only a few pixels.

It might also depend on the AI. If you spam Junk Yard Dog, and the mobile grid is around until the next trigger cycle (note, you would see it in this case, but most people use them instantly), it's possible the units will move a little bit. Some other AI's might not move them at all.

Essentially, if you can't see the grid for even a split-second, the answer is no, they won't move.

Thanks. I am running the grids instantly, so it shouldn't be a problem.

One more question: if I'm running six different mobile grids (both 1.5 and 1 grid spacing), with Hypercheck on, moving the grids several times per trigger, will it cause my map to lag? So far, I haven't had the opportunity to test it except by myself.

You definitely have the possibility to encountering lag if you are doing that each and every trigger cycle throughout the game. However, if the placement or use of grids is restricted to every couple of seconds or even only using them once every 1 or two seconds is significantly less lag-prone than if you have them run each and every cycle.

In that case, I'm probably fine. The grids are only run after the player builds a High Templar, which is not going to be very frequent.