Can I increase my iron intake by eating food cooked with cast iron?
Can you get leached iron from cast iron?  Yes

Is it consistent in the amount that you get?  No

Is it dependent on the food in the pan?  Yes

How much?  It varies hugely dependent on the food.  More liquid, acidic foods leach more.  How long its in the pan also plays a role.  3 oz of spaghetti sauce could leach as much as 5mg - that's almost 1/3 of the daily recommended 18mg.

So you can cook with cast iron to get more iron, but it will vary wildly on what you cook in it.  It will also likely increase/decrease based on how well the pan is or isn't seasoned.