The answer is yes, but first read this article.
There are some skills that can be learned through book reading while there are others that cannot be. Reiki healing is more of ability than a skill. It is to be either acquired through personal effort or received from a Reiki teacher because everyone is though born with Reiki energy but not with ability to use it at will. Born healers are very rare.
If someone wishes to acquire it through personal effort, there is absolutely nothing wrong with it. The question is that if Dr. Usui could do it himself why others cannot do it. The answer is "surely they can". Dr. Usui worked for years to find how to do it and finally succeeded but he did not reveal what exactly he did to get this ability. Only outline information is available about his studies, practices and meditations and most of that is hearsay. If you can discover the method and learn it yourself, that would be great. That might take years though.
An easy way is to receive this healing ability through a Reiki teacher. This is like getting ready-made stuff from the market. Alternately, in case of cloth for example, you can grow your own cotton, and put up all the machines and systems to finally convert that into cloth and stitch it yourself rather asking a tailor to do that for you. The choice is yours; do what sounds easier to you. Similar is the case with the ability to heal; acquire it yourself or receive it quickly from a Reiki teacher in a short time. The choice is yours.
The process to transfer this ability is called attunement. If you wish to read more about it, go to this page.