Langeveldt,
Yes, it is certainly possible to work, either full or part time, whilst training for a CPL. I've done it - I had a job in IT when I started flying, I still have a job in IT now I have a CPL, and I plan on starting a Flying Instructor course without quitting my job just yet. Not quite the same as you, since I had my job well before I got into this whole flying thing, but proof that it can be done, and there are hundreds of others out there who have done the same.
FFF
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