I'm not so sure. First, I'm not sure he'll always get to fire first, but let's say you want that - there's still a problem. And that problem is: Initiative is not just between two persons - it's between ALL the persons on the battlefield! So let's say your archer rolls init 8, your fighter rolls init 12. Now, ANOTHER archer rolled 10 (he's firing at the first archer), and ANOTHER fighter rolled 11 (he's attacking the first fighter). Now: Determine the course of action for this round (they all act in the same phase, ofcourse).
This is also the reason I dislike the "melee vs melee" mods to init. Sure, it seems to make sense, but the charging fighter with pole-arms rolls 10, the thief with a dagger rolls 13 and the archer, firing at the pole-arm fighter, rolls 12. HOWEVER, in "melee vs melee"-mods, charging with pole arms gives plenty of bonus (I think +5), so he should get to act before the thief. But what about the archer?