I would say, that yes, the cause of that fatigue is the extremely low testosterone. I have had numbers that low, and what you describe mirrors my experiences.
Testosterone alone may be the culprit, however, have they tested all of the sex hormones including the Pituitary gland? I have battled a Pituitary tumor and subsequent diseased gland for almost a decade. Please make sure the cause of the low T is not related to a wider endocrine disorder.
I, personally, switched from the gel to injections. The gel had to be used daily, is messy, and started to cause some local irritation for me. The injections have been easier for me. I dose once every two weeks. I started with a higher dosage and within a few months I was having some side effects. The worse is the edema and if you have BPH, it will make that worse as well.
We tested the female hormones and I was producing too much estrogen and prolactin, which is not uncommon on T dosing. I now take a very low dosage of Arimidex and Gabergoline. My numbers are now more balanced and my T is back up to about 450 as of my last round of blood work. The lowered dosage on the injectable ensures very little edema. After a six months of antibiotics, I have the BPH under control as well. On a lower dosage, it will take a bit longer to get my numbers up, however, I suffer only minimal side-effects this way. My Endo and I are shooting for around 750 as the magical number to reach, then we will begin cycling and doing even lower dosages further between shots.
I have suffered no other major side effects. While my libido was OK when that low, it is much more robust now. I also have more energy, sleep better, less irritability, no depression (a very common low testosterone symptom!), and I am slowly starting to work out a bit more. I have other endocrine problems and have a cocktail of replacement protocols and other medications that I must manage, so your situation if it is just low T may be a bit different.
Good luck to you!
On quick edit - I read the other replies, and a stress test is a good idea. Low T can also negatively impact the heart, and if you have had this for awhile, well, it is best to be safe. Also, they did a full cardio (EKG, Echo, & Stress Test) plus PSA and manual exam before I began injecting, so requesting that should be an easy insurance approval, as it seems to be fairly standard when starting male hormone replacement.