The game never becomes a full-blown fps ala CoD4. While the majority of your in-game actions will be killing enemies the game favors a rpg'ish-adventure'ish approach, enticing you to use the different avaiable powers, taking advantadge of the environment, customising your character and yes, ammo scarcity is part of the deal.
Still the game's very carefully built and you can finish it up from any approach. 100% gunmen playthroughs are possible, albeit harder. And yes, you could go through the whole game just by stunning and wrenching albeit it'd be painfully slow. That's the beauty of bioshock, you make what you want out of it.
Give it a rent =) It's well worth that, at least.