Looks like you can, and yes, it also looks beautiful.
(Read the update at the bottom!)
This, above, is a Fiasco table/setup as built in the new version of Google Docs Drawing. Pretty, huh?
Drawing a table like this only takes a few minutes, and you can create an empty template and duplicate it indefinitely to play again.
The “dice” are not rollable, just copied and moved around on the “table”, but that’s more than enough.
Now start that google hangout (with Extras you can use the gdoc directly in the hangout!), skype, teamspeak, or other conferencing tool of your choice, and you’re good to go.
UPDATE It seems I forgot to edit this post, but you can easily create your game of online Fiasco, now, thanks to the Google Docs Templates. Just go to the Fiasco Table Template and click the “Use this template” button.