Travel with AP with wrong DOB

[mytrader]

I have recently received my EAD+Advanced Parole card and my Green Card through marriage. However, I noticed that the Date of Birth is incorrect (It says Jan 2 instead of Feb 1). So, i returned the Green Card for correction with the appropriate documentation on the 1st of October. I am informed that the processing time for the correction is 3-4 months. However, the problem is, I have to travel on business next week and I only have an EAD+AP which has the wrong Date of Birth. If I travel with this AP document (and proof of all the documents I submitted for correction), will there be any problem with re-entry?

Please advise. Thanks.