If you find a controller/drive that will control the motor and also accepts step/direction control signals, then your setup should work fine. For it to work with Mach 3, make sure your drive has step/direction inputs (compared to analog input).
"Would a simple DRO work and be accurate enough for mach? Could Mach even control it with input from one?"
Usually, the DRO signal (motor feedback) does not connect to Mach 3...it connects to the drive. Mach 3 tells the drive what to do, and the drive sends appropriate power to the motor while continuously reading the motor speed from the feedback signal and adjusting the power. Find out what kind of feedback your motor has (encoder or resolver)...and then find a drive that accepts this kind of feedback.
One very accurate solution that won't get bogged down in steel is to go the high performance brushless AC servo route..ebay has a lot of motors (and drives) to choose from. Find a match (i can give more info on this if you want) and u'll be ready to go. AC's are maintenance free and capable of very high transient torques (up to 3-5 times normal operating power but for a short period of time; 0.1 to several seconds). There's always some nice Servostar drives for $200-$300. You can definately find a nice motor to match a Servostar drive for ~$150-$250. These drives accept both single phase and 3-phase 220VAC. When single phase it used, the drive power is derated to something like 85%. Even at this there may be enough to drive a 2-3hp motor...you can check the numbers. If not, then a rotary phase converter is a possibility (these can be expensive though ~$1000 is a good deal for a 15hp phase converter).