Is it possible to cycle from the Marco Polo Airport to the Santa Lucia train station in Venice?
Yes but I don't know why you'd do it...
Italian traffic is the worst. It is far too dangerous to be cycling in. The streets are narrow also.
The reason he would do it is because he brought his bicycle with him. That wasn't the question. I love it when the non-cycling community chips in to tell you how dangerous it is to ride a bike. Most European are far kinder to cyclists than their Am counterpart.
If you go to www.viamichelin.com, under "driving directions" you can type in your starting point and ending point, then at the bottom click on the blue options link and select bicycle. It will calculate time, distance, and a step by step route. It looks like it's about a 14k ride.