I wouldn't.

Its not just carbon, there are "ion exchange" beads - pretty much small plastic beads. Who knows what they would leach into the soil...

It depends on what this filter is removing from your water.
Most of these types of filters are Activated Charcoal, the same stuff that is used to filter the water from a fish tank. Activated charcoal, much different stuff from the charcoal used to grill with, can be composted. I doubt that a filter on a faucet or a canister would be filtering things such as heavy metals other then possibly small quantities of iron.