For anyone who wants to know. Here's the differences and similarities between Tratar de and Intentar http://www.spanishdict.com/answers/3377/tratar-vs.-intentar
You are correct. Notwithstanding that many people commonly would say "try and eat," it is grammatically incorrect. Consider that connecting the verbs with the conjunction "and" implies that one is attempting both actions independently. On the contrary, one is trying to do "something"--in this case "trying to 'eat'." If an object was included (e.g., breakfast), one could test it by determining that one was not trying and eating breakfast; rather, one was trying to eat breakfast.