Yes when you stay in the nether it loads the chunks so that the pumps will run. It shouldnt fill the tank on the other side though, unless you have a chunkloader there. You yourself are a big living Chunkloader, really. To make things run that are not within 128 blocks of you, you have to make chunkloaders.
You can pump lava through pipes to magmatic engines or geothermal generators (or thermal generators if you use gregtech). You can actually also pump it right into combustion engines, but they will run slowly on just lava. Lava is also needed for biogas engines, but not very much.
It also works in generators and solid fueled fireboxes, but Im not sure if you get the bucket back, and Im thinking that to do that you would not be able to automate the lava into and out of the firebox.
magmatic engines are the most efficient use, I think.