Yes, and in principle I like that a lot.
In practice, it's not exactly optimal. Relying on 6s for extra hits or suppression means you get them only on max ammo usage. This, in turn, increases the rate at which you need to reload (which has the same functional effect as suppression -- it costs you actions). If you are going for it on purpose, then you are also subjecting yourself to added mishap risk. There's not a very significant margin here to go into the black, really. Doing the odds like leonpoi helpfully did is beyond me right now, but I'm sure you could prove this out.
I said in the character generation thread that I'd like to see more of the specialties offer "feats" or "talents" (like Forbidden Lands does), that would offer characters with specific training more opportunities to bend and break the rules, rather than just "here's a +1." Both suppressive fire and ammo conservation seem like excellent places to do this sort of thing. Since they are specialties, you can deviate from the standard rules a bit further without big mental complexity cost, because you know they will only apply to certain characters when they do certain things.
For instance: Machine Gunner - you are trained in the art of denying ground to the enemy through continuous fire. When you shoot, if you don't roll any 6s on ammo dice, you still generate a suppression result if any two of the ammo dice you rolled add up to 6+.
Could be worded better but you hopefully get the idea.