As a refrigerant compressor the oil is circulated around with the gas
in a closed loop system, when we hack the compressor out and use it as a
open loop system the oil is lost over time anyway.
So to answer the question, to lose a little oil is not the end of the
world, and the compressor will still function.

Due to the oil loss over time the compressor will eventually run dry
anyway and fail in time, but from my experience this take a long time
and many, many, hours of use till a failure occurs.
There is always old fridges tossed out, and to source a replacement
compressor is easier than trying to replace the oil, as the oil is not a
standard mineral type oil like motor oil and is hard to acquire.
Im still yet to have a compressor seize up, and i have given a few a
fair flogging.