That's going to be a tough call...many contractors will tell you that it can be done just so they can get a large job, but when it comes time to warranty the peeling floor, they will avoid you like a plague.
You will have to find the oldest and most reputable (read: expensive) contractor in town and get their opinion first.
If I were forced to do that type of floor, I would have approached it this way:
1.)Do a complete concrete overlay on top of the existing floor, then coat epoxy. (The overlay is less suseptable to
oil or grease delamination) or;
2.)Do an aggregate/quartz filled epoxy floor. They are usually 1/4 to 1/2" thick and also resist oils and moisture very well. This would be my first choice over a simple coating.
Both methods are expensive, but are the only way I'd approach this if you want a new floor.
Or, you could have the concrete replaced completely, but that would be very messy and time consuming.