There should be little charge remaining on the rocket body during powered ascent, despite the significant charge generation.
The reason being that the rocket body forms fraction of a percent of the very large conductive body that is passing up through the atmosphere. The vast majority of it is the conductive and neutrally charged plasma exhaust from the engines, which is many times the volume of the rocket body.
Effectively, the rocket earths itself out against a very large amount of atmosphere.
Which is part of the reason why one does not launch through lightning-forming clouds. Lightning loves to be introduced to a half-a-kilometer or longer conductive rod that gets rammed through a charged cloud!