I strongly doubt that the shutter has a close connection with focusing mechanism and its speed. D700 cameras have nominal shutter release count at 150,000, but can work much longer. Check here http://www.olegkikin.com/shutterlife/ for the expected shutter lifetime. D700 is unfortunately not in the database, but you can look at the D300 data.
According to your profile you mostly use AF-S lenses that have a built-in focus motor. Therefore I would first look to the bayonet contacts if they are dirty or damaged. If yes, just send the camera to Nikon representative for cleaning.
If you noticed the slow autofocus performance with AF lenses, the culprit is most probably the "screwdriver" motor built into the camera. Again, send the camera to authorized Nikon representative for testing and possibly replacing the motor.
The third possible cause would be dirty autofocus module inside the camera. Check whether the autofocus is slow on all autofocus sensors or just on some of them. If it is slow on just some of them then very probably these sensors are dirty and need professional cleaning.
Lisa, welcome to Nikonians! Have you had a CLA - Clean, Lube and Adjust? Nikon USA or an authorized repair facility can help you there. If you let them know what'g going on with the camera, they can advise you if need replacement.
Welcome to Nikonians! The AF module and the shutter assembly are different systems therefore a problem with the AF system does not mean that the shutter is about to fail. Nikon Service in Melville NY or APS in Morton Grove, IL should have no problem getting your D700 beck to 100%. Good Luck and Enjoy your Nikons!