To what degree, if any, is the new, allegedly more secure Telegram app functional on Republic Wireless? Will it allow MMS as opposed to SMS?
Unless something I’m unaware of changed, Telegram is not intended to replace standard SMS/MMS messaging. Rather, Telegram is intended to provide a means of secure messaging (particularly group messaging) among folks all using a Telegram app. There is nothing about a Republic activated phone that would prevent use of Telegram as a means of communicating with other Telegram users. Please note, Telegram uses cell data when out, about and away from WiFi.
A similar app to Telegram is Signal. Like Telegram, Signal is primarily intended as a means of secure messaging with other Signal users. Unlike Telegram, Signal also functions as a standard SMS/MMS app and using it that way does, in my experience, work on Republic activated phones. Also, like Telegram, Signal would use cell data when out, about and away from WiFi when communicating with other Signal users. Signal only falls back to SMS/MMS when messaging someone not also using Signal.
There is no particular advantage to using SMS/MMS with Signal as messages are only secure when communicating with other Signal users. The same would be true of Telegram if it did SMS/MMS. SMS/MMS has no encryption and, therefore, cannot be secured regardless of app used.