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.
depends on your provider, but normally you get the "not-collected" emails later, with imap as well as pop.