Yep, it is important to eat during a long ride - yesterday I didn't take my own advice and was starving/exhausted at the end of it. I thought my breakfast was large enough & close enough to the ride to carry me through it - but it wasn't. Thankfully ride ended at my LBS and was able to snag a Cliff bar until I got home and ate real food.
I was so worn out at the end of my ride that my butt was still on the saddle when the bike stopped

I didn't fall over though, and was fine as soon as I had something to eat.