Some of the responses here are just so Peak Mumsnet.
Look, he's 18. He's technically an adult, his right to do what he wants, blah blah. But yes, I'd be pretty horrified. It's not a lovely and upstanding thing to do, it's bloody stupid.
He needs to be focusing his time, energy and resources on getting himself set up. Is he providing financial support (either formally or informally?) in this setup? Unless he has inherited a lot of money from somewhere, it's pretty hard to imagine an 18yo having the resources to do this without shortchanging himself. If he's working, he won't have much money. If he's in full time education, where is the money coming from right now (Mum and Dad, I'm guessing).
Even in cultures where people marry younger than we consider usual, it's pretty out-there to be the "father" of a 2yo at age 18. This is way too young to be playing the father role to a toddler.
The odds of this relationship surviving long-term have to be close to zero. I don't think he should be playing daddy to this child and encouraging a parent-child type relationship when he is very unlikely to be in the child's life long-term; nor should he be deluding this young woman into folding believing that she's got a new partner and "father" to her child.
And a very young single mother of a two year old should be focusing on her child and on setting herself up to provide for a child, not on dating and forming new relationships right now. Stepfathers and mums-boyfriends are risk factors for children--the obvious risk being abuse, but also the more subtle risk of emotional involvements between the child and the guy, which can leave the child devastated when the relationship breaks up. I'm sure the OP's son isn't an abuser, but the risk of emotional entanglement is absolutely there. This is not good for children.
Is the biological father of this child at least paying financial support? I bloody well hope so. We have DNA tests for a reason.
I hope to hell that this couple are doubling up on birth control (hormonal BC AND condoms), because otherwise there could be another pregnancy in the near future and the OP's son will be well and truly stuck.