And my camcorder doesn't have a mic input. Could I use a digital voice recorder, and a clip on mic, copy that to my computer, and sync that sound to my voice on my video?

Yep. That is doable. You would want to use a clapboard to give you an easy reference point to help you sync up your shots and audio later. (or just clap your hands loudly before you say action, would work too)
Also you may want to think about who you know that could man the audio recorder and microphone during the shoot, because if you are trying to control the camera and get decent sound simultaneously with two different devices, the quality of both will probably suffer