STEP 4A. Is low testosterone making you anemic? Yes, it can happen and, in fact, is actually quite common. Hypogonadism is known for causing fatigue and anemia can contribute.
Testosterone affects many different hormonal and metabolic systems in us men, and one of them is blood cell production. Although red blood cell creation is done primarily in the bone marrow, it is also strongly influenced by a renal (kidney) hormone called erythropoietin that is responsible for triggering stem cell involvement. Who would have guessed that the kidneys are sending messages to the bones, which in turn build red blood cells, eh? And, if you stop and think about, this means that testosterone is responsible, albeit indirectly, for delivering oxygen to every cell in your body.
Here is the key point though: when testosterone falls due to hypogonadism (clinically low testosterone), red blood cell counts usually fall as well due to the kidney hormone issue. Because of this, anemia is a fairly common side effect for men with low testosterone and can explain some of their low energy levels and general fatigue. Having your sex life go down the toilet is misery enough, but anemia will make you so tired you don't care!
NOTE: Low testosterone also profoundly affects the male brain, perhaps moreso than any other factor. It can also disturb sleep. Testosterone is the "passion hormone" and, without it, a man often feel unmotivated and zombie like. All of these factors can also affect a man's energy levels.
Of course, physicians often see this issue in some of the extreme cases. For example, when men with a pituitary adenoma are receiving anti-androgen (testosterone blocking) medications, they will often develop anemia.  And men that have chronic kidney disease and low testosterone have been found to be less responsive to erythropoietin-stimulating agents. 
For these kind of reasons, researchers were not surprised to find, then, that senior men in the lowest quartile of testosterone had a much more significant - about double - chance of having anemia when compared to those in the highest quartile. The range for the lowest quartile was 346 ng/dl (11.8 nmol/l) and below. 
This brings up a very important point. Many doctors and labs are still using 260-280 ng/dl as their standard for hypogonadism. But the above study shows that issues with anemia may start to arise at around 350 ng/dl or even higher. This underscores the importance, if you have low T, of getting your red blood cell count checked. Remember that anemia is potentially a serious issue: besides the fatigue and lethargy, it can lead to a racing heartbeat, dizziness, shortness of breath and muscle cramps. Anemia can even cause an enlarged spleen.
How do doctors usually test for anemia? Usually, they will order a CBC, which is a complete blood cell workup that includes things like hematocrit, hemoglobin and red blood cell counts. It's a common test that is usually covered by insurance, so discuss this with your physician. The doctor may also order a ferritin and other tests to make sure the underlying cause of your anemia is determined. Yes, if you are low or lowish T, that is probably the reason. But it could be other medical issues, such as an immune attack on your blood cells, vitamin deficiencies and so on.
To test their theory of the tie in between testosterone and anemia, researchers looked at what happens to red blood cell counts with men on Testosterone Therapy. As expected, administration of testosterone therapy improved red blood cell counts. 
CAUTION: Men on Hormone Replacement Therapy can have as a side effect overly elevated red blood cell counts, polycythemia, that can increase the risk for stroke. This is why it is very important that your red blood cell counts be monitored regularly by your doctor if you are on testosterone therapy. Discuss this with him or her. I discuss this issue in my link on Ways to Lower Hemoglobin levels.
3) Nephrol. Dial. Transplant, 2011), "Testosterone deficiency is a cause of anaemia and reduced responsiveness to erythropoiesis-stimulating agents in men with chronic kidney disease"
4) J of Neurosurgery, May 2003, 98(5), "Anemia, testosterone, and pituitary adenoma in men"
5) ARCH INTERN MED, JUL 10 2006, 166:1380-1387, "Low Testosterone Levels and the Risk of Anemia in Older Men and Women"
6) American Journal of Kidney Diseases, Feb 2006, 47(2):251-262, ""Transdermal Androgen Therapy to Augment EPO in the Treatment of Anemia of Chronic Renal Disease"