I-94 expiring 1 month prior to max-out date

[n0vice]

My I-94 is expiring 6-June and my max out date is 7-July. My company is willing to file an extension so I can work for this one additional month. Is this a good idea, or will it jeopardize my future entry into the US? I don't expect the approval to come through in that month, it is just a means to extend my stay here. I will have to leave prior to max-out date anyway. What happens if my extension is filed, and I leave the US before my max-out date without getting a response? In this case, when I leave, my I-94 will still have the date of 6-June. Will I be considered out of status between 6-June and 7-July (between my I-94 expiry and max-out date)