I dont think you will be laughed out of the bank but since your credit
is not perfect will get a higher inerest rate which will mean a bigger
monthly payment.
I would bring your mortgage current asap and payoff any medical bills
prior to applying or at least just bring the mortgage current and see
if you can use the cash out funds to payoff the medical bills(some
finance companies may even require to do this). Either way do not get
sucked into an ARM or a interest rate higher than what you currently
have.
Best of Luck