I've never had a problem with this. I fly back from Asia once a year and am often on two separate tickets. The Cathay desk at TPE will always through check the bags. They/ll also short-check them if necessary.

I once flew TPE - HKG - LHR - AMS with a BA ticket (the first flight being Cathay) and then AMS-BSL on KLM. Cathay checked my bags to BSL.