I think that would be by far the best idea!

As already noted, telephone line interfacing is a specialist area, possibly fraught with legal and/or regulatory issues - and that's before you even begin to think about actually doing the SMS thing!

I would certainly recommend that you get a suitable modem, and let that take care of all the line-interface and network protocol issues. You then just have to read its AT Commands Manual to determine how to use it.

You will, of course, need a modem that supports the protocol(s) used by your particular network...

There are many vendors of "embedded" modems - you are likely to get better technical documentation & support with these than with consumer products...