I shattered the screen of my Moto X (1st gen). Can I buy an old Republic Wireless Moto X (1st Gen) from someone and use it to replace my phone?
Yes you can from a place like Swappa or eBay.
But before you do check out all the warnings and precautions here: Buying and Selling Used Republic Wireless Phones
Then reactivate it as a replacement by following instructions found here: Reactivating My Republic Phone