This app was mentioned in
with an average of
it can. the original square reader was a smaller fatter square and the HW was unencrypted. This guy made a proof of concept that allows you to see plaintext of track 2 and 3. to see track 1 just put one of those grocery bag ties in the square reader and you can see that too. Obviously that's not going to be a viable or 'sneaky' hack, running someones card, then adding a shim and running it again...but in theory, yes it could work.
Hm, alright well assuming it's not an encrypted reader, what OS is your phone running? If it's Android, you can try out Rhombus, if you're on iOS I think you're out of luck as far as any ready made solutions, any other OS, I don't know anything about as far as magstripe readers.