You can't leave your tank unattended for months and have any hope of those fish surviving.
1) Goldfish produce too much waste for a well-maintained 10gal, let alone one that never gets water changes.
2) I'm not sure how quickly water will evaporate, it's affected by air temperature and surface area of the water, but I know my 30 gal tanks each lose around 1/4 to 1/2 of a gallon of water to evaporation per week. Your tank will dry up over the course of a few months, especially if you have warm summers. All the water level needs to do is drop too low for your filter to function, and it's lights out for your fish.
You should really try to give these to a friend or family member to care for, they might actually survive in that case.
If you do decide to be stubborn and kill your fish....
1) Ensure that they are in a room with a fairly consistent temperature. Summer temperature fluctuations can be significant when you realize that you won't be around to open windows and turn on fans or run the AC when appropriate.
2)Run the feeder and observe it for at least a week. The automatic feeders with the big hoppers of food make it hard to measure out the right serving size, and will take some tweaking to get it right. Err on the side of underfeeding since that will reduce the amount of waste in the tank.