In a controlled environment, for proof of concept and experimenting it should work.
In the wild, the problem is that any IR may be detected as an instruction to the PICAXE to enter its programming mode, which means it could reset and behave quite erratically; it would be similar to leaving the Serial In line floating. In the worst case, the PICAXE could enter the download mode, see something it starts to program, and leave the PICAXE with a corrupt program inside. Recoverable with a reset or another download, but the PICAXE could be 'dead' until then.
Any secondary IR could also play havoc with a genuine download attempt, and bright sunlight could also swamp the signal.
If this mechanism is used anywhere near an IR remote control ( especially IR light dimmers ), you can probably expect lots of problems.
It would be possible to add a switch to disable the IR receiver once download has been completed, and turn it on before each download. That does mean you won't be able to beam a new download into a PICAXE on the otehr side of the room without going over to enable download, but it could be a suitable comprimise.