All plants use nutrients for survival and growth, mainly being nitrates and phosphates. So any plant would be beneficial in a marine tank. They use CO2 for growth and release O2, thus keeping your tank's pH stable during the night.
There are disadvantages, it takes time for algae to grow and that "small" section might not be enough room to accommodate enough algae you need for the removal of sufficient nutrients.
Caulerpa can go into it's "sexual" stage of the life cycle (easily fixed by having a 24 hour period), however really only applies to the grape Caulerpa.
Lighting is another factor, a normal cfl globe works wonders, I currently use special LED globes with blue, green and violet LEDS, two large yellow LEDS and one cfl and my Caulerpa and Chaeta is growing like wild fire. I have heard some using T5 and T8 globes. It's really your choice.
Chaeto takes longer to grow and it's best kept tumbling in a water (mine doesn't tumble, but it's in more shallow water).
I have never heard of hang on refugiums, or do you mean an algae scrubber? Refugiums usually go beneath a tank or can be worked remotely.
Alhgal scrubbers work well, again size of scrubber is determined by your bio load. I am sure you will get others views and experience replying.
