I don't think it would be realistic to run the full blockchain on a phone so the kind of wallet he is thinking of would have to talk back to a version of the bitcoin client running on a computer you control. I suspect this one, like Mycelium, talks to a server hosting the blockchain.
(Though with Mycelium, at least, the transaction signing does occur on the phone so it should be safe for certain values of safe)
Yes, I checked the linked software. It seems to be a web wallet with an offline GUI.
Does the Android version of Mycelium work the same way as the PC version?
@mymenace - This is not even in the ballpark.
I was not aware of a PC version. On the Android version, it relies on a server to process the blockchain but the keys are kept entirely on the local phone.