It could have a bearing. Banks love customers who need loans of less than 50% of the value of a property. So (in a very specific case) if you were buying an apt for 300k and had 151k equity you would get a better interest rate than if you had less than 50% equity i.e. 120k.
In terms of actually getting approved for a mortgage they would also look at your earnings, your spare cash after you pay out for your bills, and your current loans.
Its hard to say without a more specific value for the property you are looking at and your current earnings and loans.