While I can't say I've ever heard of anyone having to eat to get work done, I do know, from years and years of personal experience, that I absolutely HAD to smoke to get anything done. Are they the same? Not sure, but my gut says "yes."
We form habits, good and bad, and they become part of whatever "ritual" we're trying to focus on, then we begin to believe we can't focus without the crutch...........
For you it's food, for me it was cigarettes, for other's, who knows. (And maybe we don't want to for that matter!)
I don't think there's anything weird about you eating while researching. I suppose it might depend on what..........and how much of it, you're eating.
When I first gave up smoking, working at the computer without my cigarettes was really difficult as it was such a powerful trigger. I began to put out stuff to munch on but realized if I kept eating all that nice, sweet, salty junk, I'd no longer fit in my chair. So I began to put out crispy veggies and a small bowl of sugar free hard candy for the really bad times.
I'm not sure I'd call what you have a "compulsion" or not. Just sounds like you feel you need to graze a little while you work.
Smoke, eat, focus, work................maybe, like me, you just need to find a different way to keep yourself focused. I do NOT recommend you pick up the smoking habit.
Just a thought.
Peace
Greenlydia