If I'm to believe Wikipedia, Blue, it can't qualify as an ICE (Internal Combustion Engine) motorized bicycle for unregistered use in Australia, because there is a power limit of 200 Watts here. That is 0.27 hp, compared with the Solex's claimed 0.7 horsepower:
http://en.wikipedia.org/wiki/Motorized_bicycle#Australia_2I must say, I've never seen a legitimate motor-assisted bicycle here with anything like the performance of the Solex.
Incidentally the Wikipedia article uses a Solex as its sole illustration of an ICE bicycle, which is in line with Kori's report that it conforms with regulations there.
As a side note, Wikipedia reports that Queensland does not permit any form of ICE bicycles - in that state it is electric power only. From some very quick reading on the US, a number of states there also only allow electric power.