Achromat and LRGB

[earth titan]

I have a good quality short focal length achromat (80mm, F6) and I'm deciding whether to keep it. Would there be any benefit to replacing it with an APO if i'm thinking of starting LRGB work in the future?

My theorising runs something like this:

Currently I have a dedicated reflector for imaging and I'm loathe to buy an APO if there is little benefit when I move over to LRGB with filter wheels etc. As the main problem with an Achromat is colour convergence, will combining individual colours negate the main advantage of an APO? Will a good APO on its own provide the same results as the use of individual filters on an achromatic?