Unsure if this is possible
 

Is it possible to have an addon where you can instantly send multiple letters if you have more items to attach than one offers?

Addons cannot send mail if they have gold or items join. It can prepare message but you'll need to clic yourself on send.

Ah, well is there an addon that allows you to do that? Or one that lets you make profiles you can use to autofill regions?

You could try DoItAll (with FCOItemSaver support) which is able to send mails if it got 6 items attached and do this as long as items are attacheable (excluding marked items).

Together with MailBuddy, which remembers your last subject and recipient, it could fullfill your request.

As Ayantir said already it will not send gold!