Writing via the Avalon master interface in assembly

Yes it sounds correct. The value you see on your component 'address' inputs will depend on the width of your component Avalon-MM Slave. For a common 32-bit wide slave, you would see a single write at address '1'. For a 8-bit slave, you would see four writes at addresses 4,5,6,7. For a 64-bit wide slave, you would see a write at address 0 with appropriate byteenables set to indicate what bytes are being written.