"Eat and go."
Translation:खाओ और जाओ ।
No, it isn't natural and doesn't make sense. Your sentence should be changed to "खा और जा" which is natural BUT the key difference is that खा और जा is for you to say to someone who is younger than you, same age as you and/or close to you relationship-wise (friends and such). Otherwise, it is quite rude to say to anyone I haven't listed. On the other hand, खाओ और जाओ can be said to people older than you, people you're not close to, and it's just more polite.
I'm so sorry!!! I completely read your sentence wrong (mentally replaced the " के" with "और")! It is incorrect because the sentence "खा के जाओ" doesn't translate to "eat and go". "खा के जाओ" translates to "eat before you go", not "eat AND go". Sorry for my mistake!