Answer: No. This is a situation where you lose even if you win. Assuming the other person is being wise, they would take your $2 and say, "I lose", and give you $1 in return. You win the bet, but you're out $1.
If someone says to you, "I'll bet you $1 that if you give me $2, I will give you $3 in return", would this be a good bet for you to accept?