Compression plays a role. High Compression motors will turn better over-all hp numbers but you may have peaks and valleys in the torque curve because the motors are alrady tuned for hp. If you have lower compression you will usually run lower boost but in doing so you will have a flatter, fatter torque curve or line as it were.It's kind of hard to increase one without increasing the other.
"Tuning for torque" is sort of misleading because in that case you are not increasing the torque as much as you are just widening the rpm range of the usable torque. You get less peak torque when you widen the torque band and lower the peak HP. However the motor feels stronger because the torque is more available.
So to answer your question, "Does adding a turbo increase the hp or the torque?" Yes.
None of these rules are absolute. you can always find exceptions so they are just general rules of thumb.
BTW there are no good engineers here. If you are looking for a good engineer I hear there is one on the CW forums who knows everything.