Actually the “wild olive tree” are the Gentiles. Israel (believers & unbelievers) were in a place where they could have life. In the fall of Israel it is the unbelievers who were cut off. Now the Gentiles are grafted in the positional of life, but Paul warns them that they too would be cut off if they don’t continue in the faith. i.e. don’t respond to God’s offer in grace. Then they will be cut off at the end of the age of grace.
Jesus Christ is the root (Revelation 22:16 comes to mind). He is the source of life and the promise of life. What we partake of today is the promise of life in Christ Jesus.
Here is something else to consider. In Romans 11:17 the words “WITH THEM,” do they refer to the Branches still connected to the Olive Tree or to the Branches broken off. The last mention was to the broken off branches. And that agrees with the age of grace. We who were cut off Gentiles are now grafted in with the cut off Jews in One Body once we respond in faith.