Air filtering system units commonly do not have a heating devise and as a result the concern becomes the fan motor. The combination of bring the capacitors to full charge and the fan to operating temperature should solve any issue regarding off-gassing. The case plastic may off-gas near /around where the motor mounts. The general low temperatures of those items should be done with any off-gassing with in 30 minutes to an hour of run time outside.
I am not aware of any filter that would require off-gassing time. It is important to remember that changing the filter become very important. NOTE: Commonly you will replace the filter more often at first, until they reduce the higher volume within the house /apartment. So, purchase additional filters now and expect to change them more often at first. Once some base level is obtained, you will find a normal rate, based on your homes needs.
What are you using for cooling?