Look at the context:
Mark 10 KJV
10:4 And they said, Moses suffered to write a bill of divorcement, and to put her away.
10:5 And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept.
10:6 But from the beginning of the creation God made them male and female.
10:7 For this cause shall a man leave his father and mother, and cleave to his wife;
10:8 And they twain shall be one flesh: so then they are no more twain, but one flesh.
10:9 What therefore God hath joined together, let not man put asunder.
Use of this passage would seem to undercut any argument you might advance to legalize gay marriage.
I think the conservative evangelicals would take your bet. You also have to contend with Paul's epistle to the Corinthians (1 Corinthians 7) which clarifies Christian doctrine in a way that is more flexible about divorce, particularly divorce between Christian and non-Christian spouses. It also fails to offer any application of marriage to same-sex couples.
Christian churches have been around for a very long time. No utterly inflexible institution can possibly survive rigid dogmatism over time and in so many societies.