First of all, welcome to the forum.
What model DirecTV DVR/HD DVR do you have?
1) If I buy one of these AM21 units, can I pipe the OTA channels into my receiver and use the DVR features, or is it not going to work since I am out of my local area.
The AM21 unit will allow you to get OTA signal from any area you are in regardless of your local area. The channels will be integragted into your DirecTV receivers guide. Keep im mind the AM21 only works with the HR21 and HR22 HD DVR models.
2) Will I be able to pick up the HD channels in general? I know the locals are not beamed across the entire country, but I am confused if I will be ok for the HD ones.
Your Salt Lake City "home" locals on your receiver will simply be a black screen when you tune to that channel. If you have the AM21 connected to the HR21 or HR22 HD DVR you will see those channels in your recievers guide. You will see them listed as "2-1". Keep in mind, while traveling you will need to run the antenna setup every location you stop to get the OTA locals in that area.