Yes.

While the game may require a constant Internet connection to run, it does appear that you will have the choice to avoid online cooperative play if you wish.

You won’t be required to partner with strangers to achieve your goals in Destiny. You’ll have all the freedom you need to blaze your own trail.

--Deej, Bungie Mail Sack
http://www.bungie.net/7_The-March-of-the-Mail-Sack/en-us/News/News?aid=1...

You can play Destiny solo, but we believe that everything fun to do in Destiny is more fun when you’re playing with friends.
-- Pete Parsons, Bungie COO

http://www.pcworld.com/article/2029986/bungie-coo-pete-parsons-discovers...