The answer will be in FAR 135 and the company Opspecs, This may be dated, but as I remember:
The above posters are correct:
A Baron is type certificated for single pilot, so unless the Opspecs specify two pilots a SIC is not a required crewmember.
Additionally, however, in the absence of operational requirements, the 135 requirements for single pilot IFR may hold the key. Unless an approved autopilot is installed and operable, a SIC is required for IFR flight under 135. So, if there is no autopilot, a SIC is a required crewmember.
As correctly stated above, 135 also specifies the training and testing requirements for SIC's.
Unless all these stipulations are met, while you will gain valuable experience and maybe a few contacts and dollars in the right seat, for logging purposes you will have to create a column in your logbook entitled "SLB" (self loading ballast.)
Your mileage may vary. This is only a starting point for your research.