You usually can, because it does not add a "Created by Photoshop CS6 licensed to CmDrKeEn, Serial-Nr ADB334455" to all of your files.
Ideally, no, you can't. The point is that you were a part of the better, more ethical social system. The Free one. Not just the convenient one.
The final design is up to your ability to execute your vision.
To have fast and powerful tools available everywhere.
If you want to show off then add a little text that says "made with FLOSS" otherwise you might want to consider weather declaring your tool of choice is part of the message you want to communicate.