3DC will look at UV tiles as UDIMs, and will allow you to import and export them. The function is currently called "Import UV Tiles as UV Sets". It was called "Import UV Tiles as UDIM", but someone (other than me) changed it back to it's old name.
That said, when you import your file, tick the box "Import UV TIles as UV Sets", and it will import all of your tiles and rename them according to their UDIMs. Then also when you're done and exporting, tick the box "Export UV Sets as UV Tiles", this will keep the UDIM imported tiles and the names assigned to them upon import.
Technically UV Sets are different than UV Tiles or UDIM, and 3D-Coat does not actually support real UV tiling or real UDIM. Using UV Sets is a sort of elegant workaround.