He may do, but what happens with year lists is that you start out strong because all the birds are new, but the further you get into the year the harder it becomes. In New Zealand (many fewer birds than in Australia!!!) I generally get about 40-50 species in January, 10-20 in February, and then it just trails off with usually only one or two species a month unless I make a trip somewhere (like a pelagic trip will net about 20 more species). The same is true, but on a larger scale, for Australia or the USA.
Vagrants certainly count in a Big Year (they are what bulk the list up above the norm - if a Big Yearer doesn't go after the vagrants then he'll be beaten in numbers by someone who does, because both of them will be getting almost all of the same "regular" birds). In the movie the great spotted woodpecker and the pink-footed goose were both vagrants.
Introduced birds also count because where-ever in the world you are, the Big Year list is based on the official checklist for that country. Established populations of introduced birds such as common mynah or tree sparrow are on the Australian list so they count. If you see a canary flying round in your garden, though, that doesn't count because its just an escaped bird not part of a recognised established population. [For personal year/life/etc lists, you can list whatever you want and organise them however you want. Some people don't count introduced birds on their personal lists. It's all just for fun really].
Usually the area covered in a Big Year is either the geographical area "owned" by the country (eg, an Australian Big Year can include the Cocos-Keeling Islands, Norfolk Island, Lord Howe Island, etc), or a multi-nation geographical unit (as used by the ABA which counts the USA, Canada, etc -- but not Hawaii, Guam, etc, even though they are owned by the USA).
I was wondering about introduced birds, because I see common starlings, Indian mynahs, song thrushes, pigeons, and Eurasian blackbirds in my yard daily, so I am already on 5. 
