可能ですよ。ワークビザで働きながらファミリークラスの永住権を待っている人もいます。
法的には、移民法22条のdual intentが適用されるケースですね。CICのマニュアルには、次のように書かれています。
An intention by a foreign national to become a permanent resident does not preclude them from becoming a temporary resident if the officer is satisfied that they will leave Canada by the end of the period authorized for their stay.[A22(2), R183] The person’s disire to work, study or visit in Canada before or during the processing of an application for permanent residence may be ligitimate.
http://www.cic.gc.ca/manuals-guides/english/op/op11e.pdf