If the AraC protein were to function as a gene repressor when it binds arabinose, would there be high or low transcription levels when arabinose is present?
A repressor inhibits transcription, thus one expects low transcription when the repressor is present.
Thus, if a protein acts as a repressor when it binds arabinose, then when arabinose is present the protein will inhibit transcription.
In the typical synthetic case of AraC and pBAD, AraC+arabinose does not act like a repressor, but an activator of pBAD. There are some awfully big caveats there, however:
- If "high" and "low" transcription levels are not well-defined, you might find yourself be dealing with a different phenomenon entirely.
- If you change the promoter or the genetic or environmental context, you may get different effects, up to and including changing the regulatory relationship.
- Transcription is also affected by other things, and so if AraC is also affecting other things in the cell, the apparent affect might be inverted as well.
Bottom line: you need to actually define the system better in order to predict the effects.