I believe you could sucessfully disregard the slack so to speak. Incidently for your overhung example, if the shaft wants to assume one position due to gravity at rest, why would it assume another position when it is rotating. In which case why do you have to factor anything into the alignmnet. This is similar to the notion that large turbines have a gravity bow at rest that will magically straighten itself out under rotation. They are made to straighten out thermal bow.
Steam turbines are a little different.
You must warm up a steamer, open the case drains to let the water out, etc., before starting and if you don't rotate it on gear it will take a thermal bow. On these really large turbine generator sets they take gravity sag into consideration when the set up the internal clearances because the sag will still be there no matter how slow or fast it rotates. It is a very common misconception , however, that turning gears are for removing gravity bow. This would be your looseness. I believe you could sucessfully disregard the slack so to speak.