I can also do this with an apple mac pro? Phones charging while off right now. ;-)
The limitation on SMS messaging in the Messages app are due to how SMS works. It is a cellular service that needs an active phone service to work. This is a separate (and older) technology than the various cellular internet services. For an iPad to have SMS service it would also need a phone number that you could call. Another words, it would need to be a phone. A few message services get around this by assigning you a phone number/service, and routing it through the internet; but most non-SMS message services are just like iMessage. Limited to internet, and their own service.
On the iPhone, Apple combines it’s own service with the cellular SMS service in a single app. Messages uses iMessage (Apple’s service) if it can, and SMS if it’s not available. On other devices, Apple will use the internet to route SMS messaging to/from the iPhone. The only (to my knowledge) exception to this is newer cellular capable Apple Watches. You have the option of registering (for a fee) your watch with your cell carrier. It will then use the same number as you iPhone to directly send/receive SMS and iMessages without depending on the iPhone.
Sorry to say, I have no idea what happens if the iPHone is turned off.
I’m pretty sure Messages on a Mac can also be paired with your iPhone for SMS messages; but since I no longer have a Mac I can not confirm this; and I’m too lazy to look it up right now.
Why is your iPhone off for charging? It’s not necessary. I’m not even sure it’s possible. Last time I tried to keep an iOS device off when charging, it kept restarting itself as soon as it had a minimal charge.