I have Directv, a HD TV and VCR. I want to know if I should be able to schedule to record a program on my VCR when I'm away from home and not have the TV on

Yes you can..

Look into Directv DVR. It will save you time and effort and will pay for itself in tape cost. And if it's something you want to keep, you can put it on the tape or a DVD at a later date.