Yes, you'll need to add the camera's current position to the newly generated x,y,z values to get the destination position for the object you're trying to draw in front of the camera.
Regarding the trig - remember that the X,Y and Z positions are all going to be affected by the current camera pitch.
In the diagram you can see how calculating the X position of the end of a line is directly affected by its angle. The same can be said in 3D. Your X and Z positions, extrapolated from your YAW angle, need to take the current pitch angle as a coefficient, since that too will affect its output.
To be honest, just by using the method described earlier to grab the XYZ position based off of the camera angles is the only code you'll likely need to do this in future, since it seems to be a pretty standard method.
I hope you find this helpful.