Hi mnmwilson,
From the site Manage your iCloud storage:
"If you run out of iCloud storage, your device won’t back up to iCloud, new photos and videos won't upload to iCloud Photos, and iCloud Drive and other iCloud apps won't stay up to date across your devices. And you also won't be able to send or receive emails with your iCloud email address."(emphasis added)
If your storage amount exceeded your allowance for that period of time, those emails may deliver once you correct the issue. It's also possible that the delivery of those messages would be rejected by the server if undeliverable. If that is the case, the sender of the message would likely get a notification to that effect.
Regards.