My employer is not a startup (financial bank) but we use a technical "noreply" account for sending automated mail to our users (no external services, they're sent through our mailserver). We use a noreply because the same account is used for different kind of notifications (to clients, to financial advisors, to internal users, to external parties etc..) and we have different inbound mail accounts for assisting them (and actually the main channels for communicating with are web trouble ticketing and toll free number, mail is not the suggested one).
Having said that, I must admit that the whole system is quite basic and not integrated as you'd expect for serious problem tracking (ideally we should use something that can keep track a problem through different channels, integrating web, mail and phone ticketing).
N.B. one problem is that unfortunately there are tons of people who cant read and dont understand that if you write from a "noreply@domain" account and write in the mail "THIS IS A SERVICE ACCOUNT PLEASE DO NOT REPLY TO THIS MAIL", you're actually supposed not to do it