Will Unavoidable Sunlight Exposure Ruin Laser Resurfacing Results?

For the first several weeks after the fractional CO2 laser treatment, your skin is extremely sensitive to the sun. So, yes, the sun exposure you are talking about might indeed be harmful, and lead to hyperpigmentation. If you are going through the expense and trouble of having this laser procedure, you have to be meticulous about post-procedural skin care, and avoiding sun exposure.
There is just no other way about it. You have to wear a hat, the one that covers your face, and avoid being outside, on the beach, etc., at least for the first 4 weeks. After that, you can get outside more freely, but you have to be diligent about sunscreen use.

I would really stress staying out of the sun right after the procedure until the redness has faded to a very light pink color.  After that - well your skin will be back to its normal state but remember the radiation effects of sunlight are cumulative.  So, while sunlight won't "ruin" your result, sunlight is one of the major aging factors to the skin. 

I live in Florida and there is now way to avoid the sun all the time.  One must live a happy and full life.  Just do the best you can - sunscreen every morning (just put it next to your toothbrush) and reapply during the day if you are going to be outside.  Avoid the most potent sunlight (in the afternoon).  Be in the shade when possible and wear a hat when not under cover.