I'm not really aware of the connection between fatty foods and the elimination rate of Methamphetamine. It wouldn't surprise me if there was a link. My understanding though is that the acidity of the urine is much more relevant for this particular drug and its relatives. A more alkaline (less acidic) urine will cause Methamphetamine to be excreted at a slower rate, leading to a more potent effect. Likewise, a more basic (more acidic) urine will lead to faster excretion.
Tums/Antacids/Baking Soda = More potent
Lemon juice/Vitamin C/tomatoes = Less potent
The food content of the stomach is going to lead to changes in the Ph of the urine. I'm sure it varies heavily based upon the food(s) involved. I would reckon that fatty foods could lead to a less-acidic environment, though I could also see how eating could stimulate the production of stomach acid leading to a more acidic environment.
For practical reasons, eating is very beneficial when you're using stimulants. It is very easy to go without food/water and not realize it. Eating at proper intervals will ultimately lead to a less intense comedown and a faster recovery. When a person is high on Amphetamine, they're not paying attention to the things that are going to make them feel better 24-48 hours from then. That's why you have to have the willpower. Tell yourself you have to eat.
Eating is always advised when using stimulants. Eat enough and drink enough. Sleep as much as you possibly can. If you're high enough that you have that "disgusted" feeling even looking at food, then it's good to have some stuff that's easy to consume.
My old standby:
Peanut Butter - Graham Crackers - Whole Milk
Take a big ol' spoon of peanut butter, sandwich it between a couple of graham crackers and shove it in. Use your milk to help make it into a paste you can swallow. Rinse and repeat and pretty soon, you've got at least 1,000 calories going, including protein, fat and vitamins. The Cracker provides you some ballast .