Am I allowed to keep or spend (non-A$) cash in Australia?

I've heard about a movement about keeping cash alive. However, am I allowed to exchange or keep "foreign" cash in Australia despite it being worth more? For example, I hoard cash via the following currencies: USD, BBD, OMR, KWD, PLN, GBP, EUR & AED to name a few and most are higher value than Australian Dollar.

I mean, will stores (in touristy parts of Sydney) accept the following in cash (mentioned above) directly for transactions. Like for instance: this item costs A$50 but gave them a 200€ (A$330) bill as payment, will they take that at face value due to that being worth more despite it being the second most traded currency globally?