I'd like to morph the question somewhat: what happens when a tank alternatively sucks in and expels fluid through the same nozzle?
The surprising answer is: it will move in the direction it would move if only fluid
would be expelled. This phenomenon is known as Machian propulsion. Machian propulsion is utilized in so-called pop-pop (or putt-putt) boats: toy boats that deploy an ultra-simple steam engine.
Pop-pop (putt-putt) boat design
The abstract to this paper summarizes the physics:
"Many experimenters, starting with Ernst Mach in 1883, have reported that if a device alternately sucks in and then expels a surrounding fluid, it moves in the same direction as if it only expelled fluid. This surprising phenomenon, which we call "Machian propulsion," is explained by conservation of momentum: the outflow efficiently transfers momentum away from the device and into the surrounding medium, while the inflow can do so only by viscous diffusion. However, many previous theoretical discussions have focused instead on the difference in the shapes of the outflow and the inflow. Whereas the argument based on conservation is straightforward and complete, the analysis of the shapes of the flows is more subtle and requires conservation in the first place. Our discussion covers three devices that have usually been treated separately: the reverse sprinkler (also called the inverse, or Feynman sprinkler), the putt-putt boat, and the aspirating cantilever. We then briefly mention some applications of Machian propulsion, ranging from microengineering to astrophysics."
Pop-pop boat engine working cycle
Video on how to build a pop-pop boat: http://youtu.be/0ki9Kta8g14
The answer to the question posed above should now be clear: when sucking in air into an empty tank, the tank will briefly tremble but not show any sustained movement. This is even the case when the tank can move without friction: the air would rush in and the tank will start to move in opposite direction, however, the inflowing air will transfer its momentum to the tank, and the tank will come to a perfect stand still.