I had a quick browse of the archive.org computer magazines section, searching for 'Australia' and 'Australian'. The sampling is unlikely to be fair, since I believe archive.org carries only what users happens to have kept and uploaded, but from this I found:
- a long-running line of Commodore magazines: Australian Commodore Amiga Review, Workbench Magazine, OZAmiga;
- a decent representation of Micro-80, concerned with the TRS-80;
- several issues of Softgold, "THE magazine for InterTAN Computer Users!", with InterTAN being the name used in places including Australia by Tandy for the equivalent of the US Radio Shack, though by 1987 it seems to be a lot more about the CoCo 3 than the TRS-80;
- a few issues of Australian Apple Review and a 1982 edition of APC with only the Apple bits retained (including a review of the Apple III) but also has solitary adverts for the Atari 400 & 800, and a bunch of CP/M machines.
I'm confident a former Commodore user has been disproportionately active but that at least suggests that the American companies — Apple, Commodore and Tandy — had a decent impact.
Addendum: having broadened my search also to include New Zealand, I've found quite a few copies of the NZ Bits and Bytes magazine, which includes a strong showing for the British micros. Leafing through the issue with "The Amstrad Arrives" as a cover story I see separate columns related to:
- the Apple II;
- the Atari 8-bit series;
- the BBC Micro;
- the Commodore 64 (with the C16 and Plus 4 being discussed therein);
- the Sega SC3000;
- the ZX Spectrum;
- the TRS-80; and
- the ZX81.
The Amstrad review notes that it "has been designed as competition to the BBC and Commodore 64 ... [i]t is also hoped to attract Spectrum users wanting to upgrade". That issue also contains positive reviews of a couple of PC clones, so it's possible New Zealand adapted more quickly to those than Europe did.
Flipping forward to 1985 (cover story: the Spectravideo X'press), columns now exist for the Amstrad, Apple, BBC, Sega, a Sanyo PC clone, the Spectravideo SV328 (the almost MSX, even more so than the Sega), Commodore, Spectrum and Atari.
An article titled "The Z-80's Finale?" notes with an exclamation mark that Amstrad ensured the new 6128 was available in NZ only ten days after the UK. Given that Amstrad were making an effort, it's likely that the market was competitive. These probably weren't various spotty grey imports.
But I think possibly your thesis is correct. A lot of major European names like Acorn, Sinclair, Amstrad intermingle with the American Commodore, Atari and Spectravideo but there's also room for the Japanese Sega and Sanyo.