No, you don't get an elite unit as a reward, just one from the current offer, see here:
Walkthrough, page 16 wrote:
You may recruit any one Unit from the offer, without paying its cost and regardless of where it can be usually recruited. You still have to have a free Command token available, or disband one of your existing Units to make room. Note: While you usually claim your rewards at the end of the turn before you resolve a Level up, you may switch the order here. If the Fame for defeating enemies caused you to gain a new level and thus a new Command token, you can use this new Command token to recruit the Unit.