Hi TIm
If you search on this forum you will find a ton of posts concerning Yosemite and mail issues. I had huge problems.
I have three accounts: Live (hotmail), Gmail, and my in-house work email. The only one that worked after I installed Yosemite was my work account, and that was only after I change my home firewall to a lower setting, which got my Live email working to.
Gmail was my last hold out. I use it to sync my calendar and contacts - former windows/android user and I just never changed. When I set up gmail I could get both calendar and contacts to work but I could not check mark the mail box in System Preferences -> Internet accounts. I tried setting up gmail as a google account and also as another account, inputting settings manually. Funny thing is gmail would show up in the mail app with my other accounts and would receive mail even though under internet accounts, mail was not checked.
I could send from all three accounts but gmail would not send emails. Finally one day I turned on the computer and it all worked. Under internet accounts the name had been changed from Google to Gmail and mail was checked. I have no idea how it got fixed but my theory is if you leave the mail app open it seems to be self healing. I know this makes no sense.
The one thing I did have to leave permanently changed was my router firewall. I had to change my settings to low (I have a frontier/netgear modem/router). I tried changing it back to medium where it had been for years and I immediately lost all mail in and out.
I know this may not help but search the forum because this is not an isolated issue and it is not tied to the mail app. I tried Outlook and had the same issues. It is a Yosemite issue and has to do with the new security measures they put in.
Lisa