Outside of Running OSX server on the Machine and running a Time Machine server (which I doubt will even work), its not possible. Time machine is designed to back up to a drive in of itself, not to a computer with a drive attached to it.
Besides, it would be a waste anyhow even if it did work... You would have to run a full computer all the time. Not energy efficient at all.
I actually continued researching and tinkering after I posted the initial post and I got it working. I enabled AFP on the old MBP, then added the external hard drive connected to it as a sharable folder/drive, then opened the time machine preferences on the new MBP and was able to use the external hard drive connected to the old MPB as the back up location.
The only drawback is that it backs up at the speed of Wireless G, since that's the type of wireless card I have in the old laptop, but the positive side is it was free. I already had the laptop and external hard drive.
Also, I really don't think the laptop draws that much energy in the first place to make it worth worrying about energy efficiency. I let it run with the lid shut (screen off) using the NoSleep app, so that reduces a lot of the energy usage, and contrary to popular belief, both old and new MBPs can run indefinitely with the lid shut and not overheat. To illustrate, I just woke up from a full night of both the old and new MBPs running while backing up with their lids shut. The new MBP was running at 107℉ and the old MBP was running at 131℉. Those are both perfectly normal temperatures. I've seen my old MBP get up to 180℉ when I was really pushing it to its limit, so it can certainly handle a sustained 131℉.
