Yes it is possible for the Rhodiola to make you sleepy. It is difficult to know how any one person may react to herbal medicines. Fatigue can be a known side effect of Rhodiola. If you have ruled out other conditions such as low thyroid, vitamin D deficiency, and low iron, and the only thing that has changed since the onset of the tiredness is the addition of the Rhodiola, then that is likely the cause. The best way to find out is to stop the Rhodiola and see if you feel any better. Then consider beginning it again to see if you feel worse. If so, then stop the supplement. If not, then I would consider further testing in the areas mentioned above.
Please let me know if you have any other questions as I am happy to help until you are satisfied.