ALL lenders have the right to do a second credit check (and confirm employment, etc) just before funding. If you buy the new car after approval (or run up your credit card balance, or anything else that raises your monthly payments) you have changed your debt to income ratio. An acceptable ratio was one of the factors in the approval for your mortgage and if you change it by adding debt you may put yourself above the lender's limit and nullify your mortgage approval.
The safest course is to NOT take on ANY new debt after approval but before closing. Don't buy a car, a timeshare or anything that would affect your debt to income ratio. You've waited this long, stifle the urge buy whatever it is for another few days. After closing, you're on your own, but don't risk your purchase by buying something now.
Any good lender will tell you the same (but you may not have been listening). If you'd like an introduction to a top-drawer lender who's been delighting my clients for years, let me know.