Absolutely, of all the Astartes Chapters the only 1 that has more influence in the Imperium as a whole is the Imperial Fists- and that's because they're the Chapter that is the most willing to answer other Imperial organisation's pleas for aid.
True Baron. in this case there are two cases of influence; influence through number (Ultras.) and influence through position (?) (Fists). Though if anything, I would have thought GW would have chosen the Fists as posterboys, being the Legion who stood their ground on Terra, while the Ultras. only arrived to pick up the scraps? Really I don't see what's to hate about the Ultras. their Primarch setdown guidelines to running the Legions, splitting them to Chapters, rules of using troops etc, is it only because they revolutionised how the Marines worked that they became posterboys?