Yes it’s possible! You can get off the plane, assemble your bike and ride to the CBD on nice quiet dedicated cycle trails all the way to the CBD. This is the best way to start your trip!

You can assemble the bikes in a quiet corner of the terminal, and then just cycle under the Freeway to Marker Rd. At the end of this (short) road there is a very nice cycle trail called the Moonee Ponds Creek Trail, this leads to the CBD and to the network of trails. To get to the CBD you will have to leave this trail at Flemington Bridge and take South on the Capital City Trail. At Docklands you can take La Trobe Street to get to the CBD, depending on where your final location is.

Please note that there is a gate against trail bikes on Marker Rd before the Moonee Ponds cycle trail, which will be annoying to pass with a loaded touring bike, so think about that detail before securing everything very safely to the bike in the airport :)