Yes. There will be an error induced because of the roll. However it's not primarily due to precession (apologies for the wording in my original post) but because the gyro is earth tied (i.e. there is a pendulous element to the erection system). Therefore when the a/c banks the gyro "sees" a false level and tries to adjust.
In more modern electrical gyros the erection system is disabled via mercury 'g' switches, while the a/c banks, accelerates, etc making them more accurate.