For more than a hundred years the weight of the atmosphere was used as a source of energy in the Newcomen engine and that surely is the point here.
The ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN has energy input (fire & steam), and alternates between steam pressure and vacuum from condensation.
The question here is will this design work as postulated and the answer is that it will.
Your system will not produce any results without any external energy source. The energy to pull the vacuum will be exactly the same as that supplied by the atmospheric pressure (minus system losses).
As RD mentioned, you could use periodic variations in barometric pressure (a few mm Hg), to supply some energy. Or, perhaps if it is and elevator, force the users to walk up the stairs, then descend using the elevator, thus with a net gain of energy. (not counting calories burnt climbing the stairs).
With no external energy source added to the system, the system as designed will consume energy due to friction, and would stop rather than generating energy.