The following is taken from PFSRD concerning temporary/permanent increases to ability scores.
Temporary Bonuses: Temporary increases to your Constitution score give
you a bonus on your Fortitude saving throws. In addition, multiply
your total Hit Dice by this bonus and add that amount to your current
and total hit points. When the bonus ends, remove this total from your
current and total hit points.
Permanent Bonuses: Ability bonuses with a duration greater than 1 day
actually increase the relevant ability score after 24 hours. Modify
all skills and statistics as appropriate. This might cause you to gain
skill points, hit points, and other bonuses. These bonuses should be
noted separately in case they are removed.
Bears Endurance goes into detail explaining that hit points gained from temporary bonuses to Constitution are NOT considered Temp HP. With this in-mind, I think it fair that the animated object would in-fact gain the hit point increase, using Bears Endurance as a template for how they are treated.