This is an awesome alternative to scraping your own bank transactions. I'm considering using this technique to automatically add rows to my personal GnuCash MySQL database.
Sendgrid has an inbound parse feature (https://sendgrid.com/docs/User_Guide/Settings/parse.html) which you can use to start building a framework - it takes any inbound email to a domain and forwards it as an HTTP request to an endpoint you specify. Used it for a few projects and its worked great.
It’s a full framework for handling almost everything a MUA would do (imap/pop, email parsing, mime parsing, sending email, etc), so yeah, it can do that. You’ll have a bunch of boiler plate code you’ll need, but a Google search will give you plenty of samples.