Can I use three phase existing wiring for a single phase a/c unit?
Yes, a new single phase system can replace an older 3 phase AC system! However there may be problems.

With 3 phase there will be a need to increase the wire size when going to single phase, so if changing to single phase your wiring may be 1.73× smaller than that required for single phase. Other than this it depends on the cost of the system and available voltage/ phases. 

Last year I installed a shaved ice maker that required 208V. We only had 480V but the transformer was much cheaper than changing the compressor. It's still working to my knowledge and was making the ice at a rate that it was supposed to.