In Single Player the Silencer is almost completely useless. Even though it allows you to get the drop on a few enemies, they'll still figure out where you are and home in on you, no matter where you are.
The silencer is much more useful in MP. Enemies usually won't be able to figure out where you are as soon as you fire, so you can get a few more shots in before they find you. It's best used with weapons that don't leave a trail or shoot projectiles, such as the Chain Gun.