I just had a motor replaced in a HVAC squirrel cage air blower. The blower now makes a kind of whistling sound along with the normal moving air sound. The sound seems to pulsate and is annoying. I know the technician has the rotor off center. I.e. there is a big gap on one edge of the housing and a very small one on the other side. Could this off center positioning be the cause?

It well could.

Make them center the cage properly. You are getting unbalanced flow that could cause the noise you note.