Can a sub be hooked up to speaker posts?

So, instead of running the sub from the amp, it would be amp, to speaker to sub.

it's implied in your statement you're using hi level connections for your sub, so yes, this is the same as connecting to the amp, except you have a little section of speaker cable in the middle.

One thought that occurred to me is if your amp is a fully balanced design, then you would NOT want to connect your sub this way (contrary to my previous statement). In this case you need to connect the Sub ground lead to a chassis ground point and not the - terminal of your speaker outputs.

However if your amp is a plain vanilla unbalanced design, then this is simply a question of which end of the speaker cable you connect the sub cable to. While the speaker cable introduces impedance, I believe it's negligible as far as when the sub sees. So to answer your question, it can be done, but you'd only know if you like the results if you compare it to connecting directly to the amp terminals.

When hooked up this way with rels how much of a load will be put on the amp.

virtually no load. The Rel has a very high impedance, and it has its own power amp and not using the amp for power, so its its effect on the amp is negligible.