Software restriction is a powerful tool, and also a fun topic:
First, to directly answer your question, there should be virtually no impact on the network itself. Software restriction is enforced entirely on the client side. The only network traffic appears when the client initially downloads the rules from the server. This is performed as part of the standard Group Policy refresh process, which would happen anyway, software restriction or not.
As for the effects on your users, it depends very much on how much testing you've done beforehand. If you spend one day collecting hashes from all the executables you can think of, throw them into a software restriction policy, and flip the switch - you're going to have a very bad day. There will always be things you don't think of: applications that copy executables into strange locations, applications that automatically apply updates (which will change your hashes), application executable that self-modify (usually as part of archaic licensing schemes, also changes the hash), etc. In a small network, the easiest way to go about rolling out software restrictions is to pick a guinea pig user (intern, etc.) and deploy the restrictions to them. You'll find 80% of your errors right off the bat.
Microsoft has a ton of literature on the topic as well. It's very dry, but a wealth of knowledge. Check out the topic on TechNet.