I use my CX bike for all kinds of purposes - trails (although try not to hit too much technical singletrack with it - carriage roads and double track are great), dirt/logging roads, paved roads and bike paths. It really is multi-purpose, and at this time of the year, is my "go-to" ride unless I am headed out for a specific MTB ride.
I say, if it fits, go for it and enjoy!
SheFly