Absolutely not. You should find the lowest priced mortgage lender (Rate, Points and Fees) and get pre-approved, not just pre-qualified. Then, when you make your offer to the bank to buy their property, they have reason to take your bid seriously. I learned in my 25 years of selling real estate, that there are multiple points to negotiate on any purchase contract...price is only one of them. And you can make a great deal on the initial cost of your home (the purchase price) and still make a terribly expensive error when you negotiate the financing.
If you make a mistake on buying your home, you can lose thousands....but, if you make a mistake on the financing, you will lose tens of thousands!
I make certain, as part of my real estate services, that my clients are fully informed and make the best choices on their financing. There are three little utilized mortgage techniques to save a ton of money over the cost of the home. Banks never offer the best mortgage rates and fees.