It makes sense, but there are a few problems with the idea- not least of which is the amount of information they would be allowed to print/film regarding the astartes missions; you have to remember that space marines routinely deal with things that the average imperial citizen would be shot for even knowing about. Added to the fact that many worlds lack the capability for mass-media distribution of information (although the odds are that in many such situations there would be Ministorum propagandist channels of some form or another), and that most people can't physically tell the difference between two astartes when they see them, relying instead upon heraldry, even when they don't wear helmets, it does make it somewhat problematic.
Added to the fact that marines are barely human, and it would appear that more suitable subjects for such celebrity status would be heroic guard officers, commissars, arbitors, navy pilots and so on (all attested to by fluff examples: Macharius, Ciaphas Cain, Arbitrator Foreboding and the pilots of Attack Run! ).
All that said- it's a big galaxy, and during the Crusade a number of remembrancers did attach themselves to notable astartes officers to tell their stories.
and then they keep nagging about the Eldar sexing up an entity like Slaanesh!