Nope, at least not with any Paypal labels I've printed.
I've shipped countless packages a day late BTW, and never, ever had one returned.
In the eBay shipping center, next to the selector for Shipping Date is a link to More Info that states:
The Mailing Date you select determines the date when your postage label is valid. An electronic record is generated on that date indicating that your package has been mailed. When creating an online label, you are responsible for providing accurate information when selecting the mailing date. You will have the option to select a mailing date up to 3 days in the future. Please note that the Mailing Date is formatted in Eastern Standard Time.
This is corroborated by the USPS notice posted earlier, though from your experience the notice should say "may be returned" rather than "will be returned." You are being given a grace period by the post office that accepts your package; others report their packages being returned, so late mailing is not something that can be counted upon systemwide.