Much depends on the exact nature of the studentship/scholarship scheme in question, and whether,for example, there's an expectation that the holder carries out some duties in return. In my own area, typically, financial support for PhD students consists mainly of a fees waiver and a sum of about €6K spead over 9 months, in return for which the candidates are expected to give a couple of hours' tutorial assistance or similar duties. Nobody expects them to live on €500/month, so a blind eye is usually turned if they take on outside paid work, within limits. But there are other, much more generous scholarship schemes (hotly competed for) and, where the sum awarded is more substantial, there is usually an expectation that the candidate won't take outside work that would be likely to interfere with their progress on the PhD. Twenty hours a week might or might not sound like a lot to them.
I presume you've read all the terms of the scheme; your potential supervisor should be able to advise you as to what's considered an "acceptable level".
Good luck with the proposal. Writing a good one is a salutory exercise in its own right.