There no reason to believe that it will not, as the arc of history appears to be moving in that direction. However, Botswana is likely to be one of the last places it will be legalized. One important obstacle to overcome first is the criminalization of homosexuality in that country.
Gay marriage was legalized in Massachusetts on May 17, 2004.
Same-sex marriage has not been legalized in Laos.
No countries in the Balkans have legalized same-sex marriage.
No country in Central America has legalized same-sex marriage.
No former Soviet republics have legalized same-sex marriage.
No, Snopes has not confirmed the claim that Sweden has legalized child marriage.
Same-sex marriage was legalized in North Carolina on October 9, 2014.
Same-sex marriage was legalized in British Columbia on July 8, 2003.
Same-sex marriage was legalized in the Canadian province of Saskatchewan on November 5, 2004.
As of December 20, 2013, about 33% of US states have legalized same-sex marriage.
Same-sex marriage was legalized in the Canadian province of Nova Scotia on September 24, 2004.
Same-sex marriage was legalized in the Canadian province of Newfoundland and Labrador on December 21, 2004.