I was wondering about this since if the enemy had that ability they would a bit more frightening, especially in FE7.
I assume that by “movement staves” you mean rescue and warp
short answer: rescue should already work but warp won’t without asm wizardry
long answer: I’ve been looking into staff ai (but mostly in FE8).
Rescue uses the same ai as physic, so it just targets allied units that need healing.
Warp, in FE8 at least, has unused ai that i don’t think works properly so you’d need to write up new ai for it.
Writing new ai for staves is already possible (I’ve done it before) but warp would be trickier since you not only have to figure out who to target but where they will warp to.
The location of ASM to determine whether AI will use a staff is known.
Therefore, I think that it works if you apply appropriate ASM.
However, efforts are necessary for that.