As PP have said, yes you can. Even without a car.
I was going to suggest taking a bus to the Boardwalk and walking to the Hess Station but that would involve a change in busses, unless you are coming from one of the parks.
Have you looked into using a grocery service? I've never done it since we always rent a car but many have reported great success doing it. And I don't believe it costs that much more than doing the shopping yourself. Besides water and sodas you can get a few more items. I just checked gardengrocer.com and they only charge $12 to deliver to WDW. Might be worth the time you'll save.
I did just do a few price checks and they charge full pop on their items-for example 12 pack of Coke, $5.89. 24 pack of Aquafina (16 oz) is $7.99. Maybe the convenience of getting it all delivered would be worth it? But just a 12 pack of soda and 24 pack of water, inc. del. would be over $26 which is over 25% of your food budget-I guess it's better if you go the Hess instead.
If you have room in your luggage you might want to pack an inexpensive toaster. We picked one up at WM for about $7 and it worked pretty well. Then I left it with my fridge swap where it worked for several years before disappearing. If you don't want to bring your own toaster, then you can use the one in the food court.
Even when we are on the
DDP, we will eat most of our breakfasts in the room. It's quicker and cheaper. You can bring many breakfast food items in your luggage. Cereal is easy to pack and doesn't add much weight. Pick up some milk at Hess or in the food court and you're all set.
If you have a collapsable cooler I would bring it with you and then you can keep things cold in the room. I've even brought along our larger soft sided cooler as one of my carryones. Used it as a tote, etc. It held quite a few things.
You can definitely order kid's meals. At CS it's no problem.
At TS it's a little trickier. We ordered kid's meals for some of our adults a few years ago at HBD and even there it wasn't an issue. However, the server did tell us that as adults, we wouldn't get the kid's soda with our meal. We didn't order the kid's meals in this case to save money, we just weren't very hungry (it was hot!) plus my 2 Dsis' didn't see anything on the regulare menu they wanted to eat.
You can get hot water in the food court. You might consider buying a refillable mug. Then you can get all the sodas, coffee, hot tea, etc. for the price of the mug. And it makes a great souvenir. They even have filtered water in the dispenser that you can get. If you have your own water bottle you could refill it at any soda dispensing machine at the parks and at POP. You can drink it straight or add a flavor tube. We go to DLR quite often and rarely buy drinks there. We usually just get free ice water from one of the CS. It's more refreshing than soda and you can't beat the price!
when you're trying to keep costs down, even if you don't like the taste of plain tap water.
