If the roof is stick framed, why would you be getting a single drag truss from a truss manufacturer?
You should be designing your stick framing for any biaxial bending and the additional induced shear/moment due to the drag loads. This may require a larger member, or it may be possible with multiple plies.
Keep in mind that unless the drag loads are low, you will probably need a 4x_ member to allow adequate edge distance from drag strut edges to strap to allow strap nailing to bearing below. Many straps will be too wide to allow a single 2x_ to properly nail.
I'm curious what would cause biaxial bending. Drag loads would add to the axial load which will be considered in bending+compression. Where would bending in the other direction come from?
Depends where the truss is located in the structure. Is it framed overtop a large window bay, where the windows are transferring wind load to the king studs, which then attach the strut above?
Due to strap installation (narrow edge of drag strut, or wide edge?), the axial load is eccentric, which causes additional bending.
