Its seems that the Greek 'logos' is similar in concept to the "Tao" of the Lao Tzu and the Taoists, however this is just a coincidence. It seems various English websites have locked onto this similarity conjecturing things about it, but asking one of my many Chinese christian friends, I have been told the word just means original reason or truth.
佈道 bou3 dou6 is announce truth = sermon
It is no surprise that Asian religions use the word, as truth is a word that religions are interested in, but as with all Chinese characters, they are so ancient they generally predate history let alone Taoists.
Additional observations based on the historical and current meaning of the pictogram (道):
Aside from my Chinese friend who adamantly denied any relationship with Daoism to John 1 in the Chinese Bible, there is no denying from my own research that there was a pre-existing religious connotation to the word through Confucianism, before Christ. Today the connotation exists in Confucianism, Daoism, and Buddhism as well as other religions peculiar to Japan and Asia. Keep in mind though as a Bible translator one would not want to indicate a preference to one of these religions over another as they are often divided by class.
The neat thing about Chinese is you see the meaning inside in the picture they draw. The composition of 道 (dào) is 首 (shǒu) meaning "head" and 辶 (辵 chuò) "go." The character 首 is distinguished by the tufts at the top, representing the hairstyle of the warrior class (a "bun"). This is used to refer to the head, such as leadership. The character 辶 (辵 chuò) 'go' in its reduced form, 廴 resembles a foot, and means "to walk," and "to go,". The combined characters signify directed, forward movement or in my words ‘going the natural and right way, using your warrior brain (male principle)’. This has eventually developed into the idea of ‘reason’ or truth as the natural right ‘path' as well as many other meanings.
However there are some things about this that makes it different from how John adopts the ‘logos’. From what I know of ‘logos’ it was a concept uniformly held by many different philosophers (Pythagorean, Stoic, Platonic, etc.) and not completely reduced to very common modes of speech. Sure every word outside of Hebrew probably has a pagan quasi-religious origin, so when writing the gospel in any language the scriptures are in some ways circumcising various words along the way and reinventing them with entirely new meanings, while extracting the true concepts from them. There are no other words to use. In the case of “logos” this was very fitting as not only did it have many elements congruent with the “truth” and familiar to all, accepted by all, but had been incorporated into Hellenised Hebrew culture through people like Philo of Alexandria. In this way John uses a very specific term and reinvents it to have a higher meaning that seems more unique then the Chinese counterpart.
It seems now that I have only strengthened the argument that the same things can be done for 道, however, while admitting the religious background that predates Daoism, and even Confucianism, this word has become to have a very, very general meaning and to imagine it will lead a Chinese person to think about Daoism would be misleading (I think as am only trying to understa my Chinese friend). This is probably why my Chinese friend thought I was crazy when I asked him.
For example, here are some other Chinese words using 道 as a ‘path’:
谷道 – the rectum
鬼道 – witchcraft sorcery
入道 – become a Buddhist monk
走斜道儿 – visit brothels
Given the widespread use, with quasi religious undertones, I think we get an approximation as to why the word is suitable for use in John 1, but why other Chinese translations might also use another one.