Depends on the data that you're trying to recover. Assuming that standard configuration is being used:
If it's related to metrics (performance warehouse - PW) and the PW is still connected, probably yes.
If it's purepath data and its was not deleted or overwritten, you should have it.
Just enable the system profile again and go back to the timeframe that you used to have data.
Let me know whether you have any more questions
To add on an additional tip, if you're looking for the session data (purepaths and visits) you can navigate to your stored sessions directory on the server and if the files have not been overwritten, they will be stored under the respective system profile folder, the default is (DT Home)/server/sessions/stored. Hope this helps.