Yes and no. It was the pinnacle in a series of bizzare behaviour from Tony while he was the Prime Minister. Certainly its the one people most remember of him. Keep in mind he ate it with the skin on as well. I think its also something people look out for, with the previous PM Kevin Rudd being somewhat infamous for eating his own ear wax on live TV.

When I was working on an archive project for the ABC, "tony eating onion" or some variation was the most common thing people searched for in the system when they first started using it.

The context: he was on a PR tour of a farm (or factory or something), and grabbed it from a pile and just started eating it like it was an apple, whilst continuing the tour. It caught the public attention at how normal he made eating a raw onion look.

When you use it to hide the breath of an alcoholic, yes.

He ate it with the skin on, too.

Yeah same. It's pretty common for restaurants and households to have raw onion in the salad (at least in north India). Unusual for someone to eat them with the skin though.