Is the study of the volunteer sector inappropriate for a labour economist? In the basics of labour economics the driving factor for increase in labour supply (for the workers in a given market) is increase in wages.

The volunteer sector consists of general and skilled labour that provide their services for free, meaning there is no wage incentive.

what I would like to suggest is that volunteer labour has to be exclusively viewed through the scope of consumer theory as income is not a driving factor for labour supply and volunteer labour must be viewed as another consumption good or service which faces utility maximising constraints.
I would agree that volunteered labor is a utility enhancing activity. Seen as a good, its price could be the opportunity cost, i.e. the wages foregone (for not working for pay). But then this is not really different from the concept of "leisure", since "leisure" in economics does not mean "fun and games", but rather "time spent not working for pay".

An interesting extension could be the potential value of volunteered labor as professional experience towards future employment for pay (in line with Arrow's "Learning by doing" efficiency concept). Then the issue becomes intertemporal, and also, income considerations arise: I want to volunteer, it generates utility directly for me, but also, I'd rather volunteer and build up professional experience that may lead to higher wages tomorrow, than try to work now and have lower pay due to smaller experience.