I was considering living in one unit in a 9-unit apartment. Since these are valued based on income, would it be possible to pay myself rent to represent the fact that this apartment should/could be valued at 9 units, rather than having income only coming from 8 units and lowering the value?
The answer to your question is Yes!
Even though you could be occupying one of the units, the valuation of the apartment building is based off the rental income all 9 units would produce.
If you have investor's and own the building through an LLC then you have to pay rent, or else it is an example of self dealing.