No, it is not necessary to wait until you are Catholic before you can pray to our Lord Jesus Christ.
He is the Lord of All and knows that you are on your way to becoming part of His Mystical Body on Earth. The Cross necklace is no problem either and a great witness to others.
New members start their studies in September and enter the Church on the Easter Vigil, in the April time period. We wish you well in your RCIA classes. If you have any questions in the process, that the folks at your parish are not answering, feel free to write us again.
Also, check out our corresponding section on our FAQ page.