What legal documents are needed for green card holders to join the Army?

I'm a green card holder, and in delay entry program for my back ground check. I swore in last December.
It requires that my green card is good for at least 6 months to be shipped out for basic training. My conditional green card will expire by the end of this year (2018) and the process would take up to 16 months for me to get the 10-year green card. USCIS will send me a document stating my status is extended for another year.
Can I use that document to prove my status to join the Army?