In my experience, your loan approval will be based on several factors. Credit rating, solidity of employment, current salary, honesty (if they feel you are being straight with them) plus the percentage of down payment.
The W2s became very important when "stated income" was used without paycheck stubs. If your new pay stubs reflect your new salary level, and especially if you have good credit and a good down payment, you should be OK with w2s that reflect a previous salary level.
I had a funny experience when we bought our home. My stock had gone up (doubled) in a short time period. Our lender asked "please explain" and I said "Intel doubled so my stock value doubled."
The W2s are used to provide historical information. Lenders typically would like to see a pattern of stability. Now, if you own your own company or you are self-employed or contract, then your W2s are more important.
However, you don't always want to borrow "the maximum" allowed. I recommend you look at how much you would like your payments to be and include property tax and home insurance in your annual calculations. Then look at the home you want to purchase, and see if you cannot make a sound decision on amount of loan you wish prior to getting a loan for the maximum your new salary warrants.