"So if you have no righteousness, do you have Christ?"
Are you meaning, if someone shows no righteousness (shows no evidence that they have Christ) do they have Christ?
I'd say no. There should be some evidence in a person's life that they are true believers in Christ. Just walking the aisle and making a confession and then living and thinking just like the world for the rest of his/her life should not give that person and or anyone else assurance that that person is really saved. When God starts a work in a person, he finishes it.
Phil. 1:6
And I am sure of this, that he who began a good work in you will bring it to completion at the day of Jesus Christ.
Eph. 2:10
For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.
God will not leave his children wallowing in sin and comfortable with that. He will be on them night and day, disciplining them, continually convicting them, but all through mercy and grace, and not with wrath, or not with condemnation.
Romans 8:1
1There is therefore now no condemnation for those who are in Christ Jesus.
Hebrews 12:5
“My son, do not regard lightly the discipline of the Lord,
nor be weary when reproved by him.
6For the Lord disciplines the one he loves,
and chastises every son whom he receives.”
7It is for discipline that you have to endure. God is treating you as sons. For what son is there whom his father does not discipline? 8If you are left without discipline, in which all have participated, then you are illegitimate children and not sons. 9Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live? 10For they disciplined us for a short time as it seemed best to them, but he disciplines us for our good, that we may share his holiness. 11For the moment all discipline seems painful rather than pleasant, but later it yields the peaceful fruit of righteousness to those who have been trained by it.