Why do iMessages sent when I'm offline (no cell or WiFi) not come in when I reconnect to WiFI but do eventually when I reconnect with a cell tower?

There are two types of messages:

• iMessages, which can only be exchanged between iPhones and not between your iPhone and other types of cell phones such as androids or dumb phones
• SMS/MMS messages that can be exchanged between all phones, regardless of manufacturer

iMessages will work over Wi-Fi, but SMS/MMS messages require a cellular network connection. Thus, any messages to or from non-iPhones will not be sent or received until you have cellular service.

One partial mitigation is to contact AT&T and enable Wi-Fi Calling; this will allow calls and SMS when you only have Wi-Fi and don’t have a cell network signal.

Another is to ask AT&T for a microcell; this is a small cell “tower” that you keep in your house, and connects to AT&T over Wi-Fi.

And yet another is to see if there is a better network provider for your location; the other two US primary carriers are T-Mobile and Verizon; both have better coverage than AT&T.

This issue could be related to the way iMessage handles message delivery and synchronization between different devices. iMessage is designed to work seamlessly across Apple devices, utilizing both data/Wi-Fi and cellular networks to send and receive messages. When your iPhone is offline with no connectivity (neither Wi-Fi nor cellular), the messages might not be received or synchronized immediately.

You do not need any cellular data or internet over WiFi to send SMS.

It will turn from Blue to Green if you have enabled "Send as SMS" and whenever your iPhone is not connected to the internet it is sent as SMS (green) to all iPhone users as well.