Would being a teaching assistant influence your research?
A 20 hour per week teaching assistantship is fairly common in the US.  In some departments TAs actually work less than the full 20 hours per week, while in other departments the actual work load really is 20 hours per week (of classroom teaching, preparation for teaching, grading, office hours, etc.)  This varies somewhat by discipline and across universities.  In mathematics, TAs traditionally have heavy workloads.  From what I know, the patterns are fairly similar in Australia, but you would have to determine how things actually work in the department where you will be studying. 

Yes, having to work an actual load of 20 hours per week as a TA will slow down your research compared with a Research Assistantship (20 hours per week working on your thesis and closely related projects) or a fellowship (no work requirement.)  However, it does pay you, and the experience in teaching can be valuable.  

Students working as TAs often take fewer courses per semester than students on fellowships.  For example, a TA might take 9 credit hours of courses while a student on fellowship might take 15 credit hours.