Your iPhone will automatically send an iMessage text as an SMS to a recipient if the message has not been successfully delivered in a set amount of time. If you know that the other person won't be able to receive the iMessage, you can skip this time by holding on the message, and selecting the send as SMS option. After doing this three times in a row, your conversation with that person will default to sending as SMS until the other person begins to receive texts through iMessage once again.
If you want to only have texts being sent and received through SMS rather than iMessage, you can deactivate iMessage through the iMessage settings in the Settings App.
Seems to be no publicly released information, probably cause there is too many factors for it to be the same with all device. Assumption would be it depends on how long it takes for the device to determine there is no Wifi connection on either end and the time afterwards to send it as a text message. This entire process would be dependent on the current network connection (if you have one and it is stable) and a good cellular signal.
In my experience, the feature is erratic at best. I've had it show up in seconds. And, I've seen it take a number of minutes. If the person has another device logged into the same Apple ID, the option may never show up. The bottom line is that iMessage is designed to have a constant connection. If someone frequently doesn't have a data connection, it's usually better to turn iMessage off entirely and just use SMS.
iMessage send as text option, how long before it reverts to SMS?
