I would not recommend it. I took my mine when she was about 6 months old.
1st, yes you do have to have a ticket.
2nd, Better buy two extra tickets to have the room for diaper bag, comfort, etc. Neyland is known for holding 100,000 but not comfortably.
3rd, Carrying he/she to the game is bad enough, holding them for 3.5 hours and then walking back carring them is worse.
4th, wife ended up sitting in under the stands to keep her out of the heat. So after the game I had two miserable people to deal with instead of one.
5th, the people around you (tennessee or other) may get stupid
6th, hey man, they are 2 months old...enjoy them while you can, watch from the comfort of your home and make their first visit a positive one!
Go VOLS and congrats on your little one!