Replacing compression fitting with push-to-connect
If possible I would cut the copper right below the compression ring as most times the pipe deforms slightly or worse if it was put on at an angle and then tightened. This might cause it to not seal properly when the push fitting is installed.

Otherwise its a gamble -- but not a bad one, if it leaks just pop off the push on connector and the cut the pipe. 

If you have never used the push on connectors make sure you have the little plastic tool so you can pop it back off otherwise you'll be stuck.