Why not? AFAIK you don't need an "SIC type" to log SIC if the plane requires two people up front. (I don't know if a Jetstream does or not). And someone will know better than me... but could if be logged as "PIC/Dual Received" if the ATP in command can instruct in that plane towards a type rating (don't flame me too fast, I admit I don't know off hand)?

If he's a MEI that will give you some more option.