Assuming his application actually got there (didn't get lost in the mail), and it hasn't been rejected without his knowledge, I believe it would be legal for him to work, but he doesn't have proof of it, so he won't be able to satisfy the I-9 requirements for any employer to hire him as an employee.
The regulation regarding automatic extension of EADs says the employment authorization is automatically extended as long as the renewal application is filed before the expiration date of the EAD.
8 CFR 274a.13(d)(1):
Automatic extension of Employment Authorization Documents. Except as
otherwise provided in this chapter or by law, notwithstanding 8 CFR
274a.14(a)(1)(i), the validity period of an expiring Employment
Authorization Document (Form I-766) and, for aliens who are not
employment authorized incident to status, also the attendant
employment authorization, will be automatically extended for an
additional period not to exceed 180 days from the date of such
document's and such employment authorization's expiration if a request
for renewal on a form designated by USCIS is:
(i) Properly filed as provided by form instructions before the
expiration date shown on the face of the Employment Authorization
Document, or during the filing period described in the applicable
Federal Register notice regarding procedures for obtaining Temporary
Protected Status-related EADs;
(ii) Based on the same employment authorization category as shown on
the face of the expiring Employment Authorization Document or is for
an individual approved for Temporary Protected Status whose EAD was
issued pursuant to 8 CFR 274a.12(c)(19); and
(iii) Based on a class of aliens whose eligibility to apply for
employment authorization continues notwithstanding expiration of the
Employment Authorization Document and is based on an employment
authorization category that does not require adjudication of an
underlying application or petition before adjudication of the renewal
application, including aliens described in 8 CFR 274a.12(a)(12)
granted Temporary Protected Status and pending applicants for
Temporary Protected Status who are issued an EAD under 8 CFR
274a.12(c)(19), as may be announced on the USCIS Web site.
When it is filed is determined by the "received date" of the application, which is when USCIS officially received it. It will say on the receipt what the "received date" was, so he won't absolutely know that it was before the expiration of your EAD until he gets the receipt. However, the "received date" is generally no later than one or two days after the mail was actually delivered to USCIS, so if he mailed the application two months early, and especially if he had tracking on the mail to know that it arrived well before the EAD expiration date, he can pretty much be sure that when he gets the receipt, it will show that the "received date" of the application will be before the EAD's expiration date, which means he was working legally.
However, for completing the I-9 as an employee, either as a new hire or for reverification since his previous employment authorization ended, he will not be able to satisfy the documentary requirements until he gets the receipt.
The chapter (Chapter 4.2) of the Handbook for Employers M-274 which talks about how to handle automatic extension of EADs says that expired EAD in combination with the I-797C receipt for the renewal application serves as a List A document for the I-9 documentary requirements. Without the receipt, he doesn't have the documents to satisfy this. In addition, the employer is required to verify certain information on the receipt in order to accept the automatic extension, which cannot be done if he doesn't have the receipt: 1) that the "received date" on the receipt is before the expiration date of the EAD, and 2) that the category on the receipt matches the category of the EAD.