No, higher interest rates would cause an appreciation. Higher interest rates would make it more attractive for foreigners to invest in Australia (as they can get higher returns), increasing the demand for AUD.
Higher interest rates make it harder for firms and individuals to borrow, reducing the level of consumption and investment. Thus economic growth is expected to contract and inflation will fall. This is the main effect, and it's why the RBA will raise the cash rate if inflation is too high.
However, as a secondary effect, higher interest rates can lead to an appreciation and thus reduce imported inflation (imports are now cheaper).
Higher interest rates also curb spending since either a) offers more incentive to save; or b) higher loan repayments (reducing free cash flow). Both of these reduce inflation though.