Not OP, but I believe it falls back to SMS if there isn’t a response from Apple’s servers, not the end user’s device. In this scenario the iMessages are sitting there waiting for a registered device to check in to send them to. (Same thing that happens if your battery dies. iMessages go into a void until some place to deliver it to.)

Yes it does fallback. There are two situations where it does so

1. The sender cannot connect to the imessage server 2. The receiver does not connect to the imessage server, on any of the devices registered to receive at that particular address.

I know both methods happen since I didn't used to have data and I would receive SMSs when someone sent me an imessage and I was out and about.

I think that's if iMessage can't reach Apple's servers. Otherwise that wouldn't make sense; simply being without a cell/wifi signal, or having your phone off, for a few hours, would mean anyone messaging you would be sending a bunch of SMS fallback messages.