X.O.
Yes, it is very possible. While it used to be that they wouldn't assess a child for ADHD until 7 yrs old, in the past year or so they've started recognizing that they can actually catch it and intervene earlier.
My son is about to start Kindergarten, and I am certain that he has it. He hasn't yet been diagnosed, but we are switching to a new doctor who takes ADHD seriously, so we will be working together with his doctor and teachers to assess him.
My son is a sensory seeker - when he is tired he spins himself (but doesn't seem to get dizzy). He overloads his mouth (still, at 5 1/2 yrs old). He touches EVERYTHING in sight including cactus leaves at the grocery store (OUCH!) He likes to be squeezed and to put heavy pillows on top of him.
My 3 yr old son is also active, but no where NEAR what my oldest is like. I think most parents who suspect their child has ADHD are probably right. We don't just say it because we're looking for an explanation or way to make things easier. We see a genuine difference between our child and their peers, and it is after a lot of investigation and soul-searching that we come to the realization that they may have a problem that no amount of discipline can solve, and then we look for a medical opinion. Go with your gut and speak with your pediatrician.
ETA: I came across this site the other day, and found it very helpful. Their videos are extremely informative. http://www.caddac.ca/cms/video/parents_player.html
ETA2: this might also be helpful: http://www.additudemag.com/q&a/ask_the_add_medical_ex...