No, you need to see where you are going and if your head is down, your helment catches air in the back.

A lot of people have this problem, try giving a slight twist of your head so one eye is higher, sometimes that helps, sort of pirate style.

It takes strength to hold up your head, it weighs a lot. In time you will develop the muscles.

BUT--if you get radiating pain or pain after cycling that doesn't subside, perhaps you have a pinched vertabrae, it's common for cyclist to get this after riding for a long time, crashing seems to aggravate it also.

I laid it down a couple weeks ago and my neck is still stiff, I hit on my side but there always seems to be some whiplash action. What a dumb sport.

I have problems with pinched nerves from years of racing in drop bars, I think the action of pulling with the arms and back while craning the head upward to see up the road leads to this problem. I was able to get relief from some exercises by a guy named Mckenzie, it got to the point where my arms would burn and go numb and I couldn't sleep, now it's manageable.