Short answer: No (to getting 'any' accounting job)
Longish answer:
You'll probably be able to get a job, but don't expect anything exciting or exactly high-paying. Accounting is a diverse profession, and it can become quite complicated, with all the legislative and common law implications, not to mention international and local accounting standards. I assume you don't really study this in TAFE and it takes years of experience before one can come to a solid understanding of these implications and more.
But yeah, I have friends who worked in Accounts Receivable even before they started studying. Pay's not great, but it's a job that they got without ANY real qualifications. Sure beats Maccas or whatever.
Your best bet is probably book-keeping however.
I'm studying accounting, with a professional accounting extension and regulations (for tax) minor. Hoping I can get myself a nice graduate position when I graduate and end up working in tax, going for my CA.
In terms of training, almost every employment offers some form of 'training', as each business/department differs from each other. But I doubt a good employer would hire someone with no knowledge/unable to pick things up on their own. I'd worry about getting a job before I worry about training.
Who knows, if you're good enough and show you work well, your prospective employer might even pay for your tertiary studies, it happens. Best of luck.