If it's a, Redding, Competition seating die have the sleeve reamed with a 243 ackley improved reamer and it'll now be a 243 ack imp Comp seating die but with the body taper being different, bigger, on your 243 ackley, I don't think the case will go up inside the die far enough to seat the bullet properly and, depending on how much clearance you have, you may get a stuck case.
I have a couple Redding Comp seater dies I had reamed to match my "improved" case because Redding only made a comp seater for the standard, non improved, version of what I have.
A standard 243 seating die sleeve or even a standard 243 seating die will NOT work with the Ackley shoulder. If its a Redding Competition or a Forster seating die you can have the sleeve reamed by the factory or by a gunsmith. Standard seating dies with no sleeves are hardened and you would have to talk to the manufacturer about having them modified. Hope this helps!