ARMS invented the picatinny standard for mounting rails, so any picatinny standard ring will mount properly on an ARMS picatinny mount (like the #18). If the aimpoint ring you are refering to is the #22m68, it should have no problems at all. I'd mount the ring on the furthest forward position.
The ARMS #18 mount for the M14/M1A does not come with rings. It is an outstanding mount by the way. The lowest possible mount for the M1A that allows iron sight use. Where others raise the mounting platform high enough to sight under the mount, ARMS, lowered the platform so you can sight through the groove in the top of the mounting rail. By using ARMS #22 rings, you have a clear channel down the center that aligns with your irons. It is a GREAT system, probably as solid as the Brookfield system.
One caveat. I do not know if the #22M68 rings allow sight through when mated with the #18 mount since the #22M68 was originally developed for the M16 family. I'd email ARMS and ask them.