I was a bit uncomfortable about this approach, as I dug in further, I became more cetain that it is not Biblical, nor is it effective.
In my many years, I have had several discussions with several people regarding faith, the Bible, Jesus, God, etc... but out of all those, there is only one that I can knowingly attribute to 'preaching the gospel without words'. That doesn't mean we shouldn't preach the gospel without words, but it does mean we shouldn't use that as our sole approach.
What's the problem?
Part of the problem is our fallen nature, we all sin, and thus do not give a perfect reflection of the gospel. We all give examples, at times, that turn others away from the gospel, rather than towards it. This phrase can be used to challenge us as Christians to seek to live a better life, striving to keep ourselves from being corrupted by the world. Yet, none of us will live up to this.
Another problem is the Biblical example. Look through the New Testament for sharing the gospel message, by and large they are all using words. Consider Peter sharing with the message with the Jews where 3000 were added to their number that day. Consider Paul sharing the gospel, using the 'unknown god' to trigger an explanation of the God who created heaven and earth, and many others.
The biggest problem is the direct command to preach the gospel in many different scripture passages. Consider this passage in Romans that speaks pretty directly to this:
Romans 10:13-14, "for, "Everyone who calls on the name of the Lord will be saved." How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them?"
Our Culture
Please don't accept this philosophy, the more we do this, the harder it is to distinguish Christian behavior from that of our culture. (yet one more reason it doesn't work)
Despite this approach not having Biblical support, and not being very effective, this is exactly what our culture wants us to hear. They want us to hear, "don't tell us about your religion". This goes right in line with the other phrases which seek to silence Christians, "we must tolerate others' beliefs", "we all worship the same god, we just follow different paths", "it's not a salvation issue", "I don't want to be prosletized".
These are all designed to keep us quiet, so we don't preach the gospel. It makes them uncomfortable. To those living without the gospel, they should be uncomfortable when faced with their sin. They don't like to be reminded, yet we have the only message of hope for them.