Nope. The experience they start with represents what makes them heroes in the first place (and accounts for their generally superior stats). They only roll improvements based on experience they earn in game play. So the captains start with 20, and need four points of experience before they roll for improvements (when they hit 24). A champion starting with 8 gets his first improvement roll after earning three experience (because he hits 11).
That's one reason why promoted henchmen can make really, really good heroes - they have better stats than the "youngblood" types, but have a ton of quick improvements ahead of them if they are promoted when they hit two experience (improvement rolls at 4, 6, 8, 11, etc.).
It is best to ask questions like this one in the "Rules" section, since not that many people check out the introduction threads (at least, not that many people comment on these threads).