I think it will differ from aircraft to aircraft and is a function of the airflow across your horizontal stabilisers on the tail. Some aircraft have two on the tail boom, some have one big one on the tail.
You would think that accelerating the horizontal stab (which is what you are doing when you yaw it) would increase its Vsquared and then produce a nose pitch up (since it is designed to minimise fuselage attitude changes as speed increases) and on some aircraft I think this is exactly what happens, even if the effect is temporary as Jellycopter indicates.
The downwash on each side of the disc in forward flight is not the same because of the AoA distribution according to Prouty.
Additionally, on aircraft with two horizontal stabs there may be different trim tabs, gurney flaps etc.
So a combination of stab design and downwash variations, I believe, means that the nose will pitch up (perhaps only briefly) yawing one way and pitch down going the other.
Many aircraft require subtly different attitudes to maintain speed in turns from one way to the other which may well be due to the same effects.