That's kind of a loaded question Silver. If you want a complete understanding than real this whole post. Basically, even if someone has had sucess... it doesn't mean you would. This post might be a bit boring at first... but... trust me... it will make sense when you get to the end... (but don't skip... lol)
It really depends on both the coating that is down and the adhesive that you're going to use. If the coating contains free silicone (which alot of cheap paints do) then the adhesive may have a difficult time bonding. If the adhesive is modified with an Organometalic or Silane type adhesion promoter it may work anyway. However, even if the adhesive sticks to the coating, the coating underneath could disbond later.
Most likely, the coating that is down is an acrylic if it's a non-epoxy. Acrylics don't have the adhesion that epoxy does. In addition, it's going to be microporous at minimum. If you have hydrostatic pressure under your concrete, the pressure escapes through the pours and the low adhesion of the acrylic paint doesn't matter. However, if you start covering up pours with adhesive and VCT tiles you minimize the opportunities for the pressure to escape. So, imagine that you have pressure coming up through your slab and the coating that is on there now is like a piece of wood shelving with about a thousand holes drilled in it and it's taped to the floor with scotch tape. Then, you screw the same size board on top of the one with the holes and block them off. The pressure is going to take the path of least resistance. It's going to build up until it's got to break the screws or the tape. Obviously it's going to break the weaker bond (the tape=the coating).
So, here is what you can do and what the risk is:
1) Do a test with the adhesive on the coating to see if it sticks.
2) If it does stick... do a test to see if the coating has good or poor adhesion to the concrete...
If the adhesive sticks and the coating appears to have good adhesion.. Then, the only risk would be delamination due to hydrostatic pressure. If you are careful not to use too much adhesive you would minimize the risk.
Let me know if you have any questions... I miss alot of posts here...
