Once again, YES. Fluid is cheap compared to parts. If you don't know the service history, I would always recommend a full Stage Zero fluid service so you know where you are starting from.
If the diff is whining, then it is likely that some damage is already done. I would start by draining the gear oil in the rear diff and inspecting for metal glitter. If it has metal contamination, start searching for a new (or used) rear diff. If the fluid looks clean, proceed with a full fluid service (gear oil, and AOC fluid/filter). Be sure to find the source of the leak and fix it.
If you do all that and still have the whine, I would look at the front bevel/angle gear. In fact, you should replace the bevel gear oil on the same service interval as the rear diff anyways.
Here is what I would recommend for drivetrain fluid services.
Transmission fluid - 3x drain and fill every 30-50k miles, depending on climate and driving conditions, More heat and more stop and go traffic = more frequent changes.
AOC Fluid - every 25-30k miles. It gets dirty surprisingly quick.
Gear oil (front bevel and rear diff) - every 50k miles. This one is probably the least important as long as there are no leaks.