Yes. You would probably even be conscious for at least 10 seconds on the moon. It would be very bright in the sun for your skin, already uncomfortable from the lack of pressure would start to get sunburn rapidly. However all the moisture on your body would be evaporating/boiling off at a very nearly instant rate taking heat with it. This would be very noticeable for your eyes and your mouth and nose which would dry out fast. It will also be the last thing you will be aware of before you pass out.
That is Leblanc. He worked for NASA. Back in 1965 he was exposed to vacuum for about 30 seconds. He passed out at the 15 second mark. He did not have ANY distress or discomfort. The last thing he recalled was the saliva bubbling off his tongue.
They repressurized the lab and he awoke to concerned technicians but had no lasting harm. His impromptu independent research gave us our best and really only exposed human to vacuum data.
NONE of this will be your problem very long and you will pass out quietly between 15 and 30 seconds after exposure to vacuum. You would be able to breathe but nothing would come in when you inhale and you would exhale all the gasses in your lungs when you exhale. This depletes your body of all gas and that is headed to your brain and will cause rapid unconsciousness.
The really big thing is that this is all very peaceful and without production or consternation. You don’t explode, you don’t freeze solid, you do not have any respiratory distress. You just keep breathing mostly unaware that something is wrong, a slight tingle, sounds becoming muffled, an odd feeling of saliva bubbling off your tongue, and you pass out.
The exact time for how long it takes to pass out is going to be dependent on how fast your blood is moving and how fast you are exposed to total vacuum. Each heartbeat will pull degassed blood closer to your brain and when your brain gets a full dose of that you will pass out.
All of the massive affects that movie portray are for the camera and not based on fact.