If you have good credit the both of you should get approved, but here is the kicker buying a house is a huge commitment and from personal experience if the two of you are not for sure that you can handle such an investment I would not do it.
Also If one or the other defaults in paying half of the house payment the other is still responsible for the payment and if you split you either have to buy their part, sell your part or both put the house up for sale and pay the remainding balance on the home and if any money is left over then you have to split it.
No being engaged don't make a difference.
Remember that if you decide to do this that you will be in a loan for 20, 30 or even 40 year loan.
Before you make a decision thoroughly talk this over and exhaust every option that you have and find the best mortgage rates and loans possible.
Hope things go well.