Some weeks ago I had the same question and the answer is YES for the version used with 1.02 Firmware.
I don't know for the new version because I haven't use it yet.
yes you can once its unlocked your done unless you restore then your going to have to put that program back ad unlock it again
Just to clarify: Yes, you can delete AnySIM from your phone after unlocking, just remember that if you are going to unlock again you need to put it back in (but there's no problem because it's probably going to be a new version, so no need to keep around the old one.)
And also, unlocks by AnySIM 1.02 ARE restore resistant; however, unlocks by AnySIM 1.1 ARE NOT restore resistant (this is due to a change in the unlock method) but you can still unlock afterwards.
So hypothetical question then... if I took a 1.1.1 firmware and unlocked it (downgrade, upgrade, activate and jailbreak) can I restore my iPhone using iTunes and then be able to redo the whole process?