Using poker chips as a means of tracking isn't a new idea. Lord Kilgore blogged about it here. But I don't know that I've heard anyone talking about using them to track ammo on an encounter basis.
Arrows, sling bullets, and darts are an important part of the resource management aspect of adventure gaming. But you don't want to get bogged down keeping tallies of everything. And you certainly don't want to end up rolling saving throws for every arrow to see if a player can recover it after use.
Here's an easy solution. Like many of them for adventure gaming it involves abstraction. Give the player five poker chips and have them give you one after every encounter. When they're out of chips they're out of ammo.
You can adjust the number of chip up a little, but keep in mind an archer can get 2 arrows off a round and if you have multiple round encounters they may be using quite a few arrows. So, I think it is a fair trade off for the ease of use in play.
You might do something similar with spell components if you want to be a stickler with magic-users.