No. The pet parent needs to provide you with enough of the food that the pet is used to for the duration of the booking. Most pets don't cope well with a sudden change in diet, so eating their familiar food while you are caring for them is the best option. Make sure you discuss this during the meet and greet.
If it's not possible for the pet owner to leave the required food, they can leave you a kind of “allowance” so you can buy the food as needed.