Short answer. No. Rule 13, Section 15 says electronic service is not effective or complete if you actually learn it did not reach the person served. A bounce-back is exactly that kind of notice, so you cannot treat the email as valid service and must serve the pleading through another mode instead.
What the law says
Electronic service is complete at the time of the electronic transmission of the document, or when available, at the time that the electronic notification of service of the document is sent. Electronic service is not effective or complete if the party serving the document learns that it did not reach the addressee or person to be served.
Rule 13, Section 15 — Completeness of service. Read the full provision →
The general rule for electronic service
Rule 13, Section 15 treats electronic service as complete the moment you send the transmission, or, where the system supports it, the moment the electronic notification of service goes out. That is the default rule for email, and it is what usually lets the sender move on without waiting for a reply or a read receipt from the other side.
Why a bounce-back changes the answer
The rule carries its own exception, and it is the one that matters here: electronic service is not effective or complete if the party serving the document learns that it did not reach the addressee or person to be served. A bounce-back message is precisely that kind of actual knowledge. It is not a case of the other side silently ignoring the email or claiming after the fact that nothing arrived -- your own mail system told you delivery failed. Once you have that notice, the completeness the rule normally grants at the moment of transmission never attaches, because the exception is triggered before it could.
What this means in practice
Because you learned the email failed, you cannot rely on the date you clicked send as your proof of service. Treat the attempt as if it did not happen for service purposes, and serve the pleading again through a mode that will actually reach the other side -- personal service, registered mail, accredited courier, or a fresh electronic attempt to a working address, whichever the circumstances allow. Filing anything with the court that represents the bounced email as completed service risks the pleading being treated as unserved, which can affect deadlines that run from service.
Keep the bounce-back itself
Save the bounce-back or delivery-failure notice. It is the evidence that shows you had actual knowledge the transmission failed, which is what triggers the exception in the first place -- and it is also proof, if the other side later claims you served nothing at all, of exactly when and how the first attempt went wrong and that you moved promptly to correct it.