No for there must be 1 female and 1 male tributes. It'll probably work if 1 female volunteer(wanting to help male contestant) and 1 male volunteer (wanting to help female contestant) make a deal to volunteer for same gender contestant if other dose the same. But no way can there be 2 people of the same gender (and district)enter the Hunger Games.
I doubt they'd accept it, because they couldn't ensure that there'd be another opposite gender volunteer for the other tribute. They'd want to keep the balance of one male and one female tribute per district per year.