Not enough storage for emails! So my iCloud email told me I didn't have enough storage. I couldn't send or receive emails. Which I just realized I wasn't getting any new emails. I just added more gb. My question is will I never get those emails sent out during the time I didn't have enough storage?
In general - it depends on how long you missed emails.

A call to Apple Support would get you specific information about your account as well as an answer. You can also try sending yourself a message from another provider to see if you get a hard bounce error or if the message queues.

With iCloud - my experience is you get some leeway and Apple stores messages for a short amount of time (days to a week) for you to realize you are full and then clean up space. They block sending immediately so you notice the error condition and seek help.