A quick Google shows that the me102 tape unit is a cassette drive and interfaces with the controller using 2400baud RS232 serial comms and the command interface appears to have a file structure so I'd guess you can get several programs on a tape. Tbh unless you have the tape unit already the cost of acquiring one and getting it to work could be more than a mach3 conversion.

There is a doc available from Heidenhain giving the block protocol so it would be possible to store programs on a PC if you have the knowledge to write the necessary software. Again a quick Google suggests this has been done before, but nothing recent within 10y.