I do not think we can determine anyone’s motivation for advertising anything. It does seem strange to many to see Jesus advertised on a billboard. Even in Hong Kong where I live, it seems out of place but there are a couple skyscrapers that have a big sign saying ‘Jesus is Lord!’ At many sporting events I have seen people have signs that read ‘John 3:16.’
Advertising Jesus in a way that might seem abrupt and not called for is common for people who have an enthusiasm about sharing their view of the gospel. For example, in conversations I have noticed people who are enthusiastic about the gospel bring it up in the conversation when it does not really seem to fit. Nothing before or after in the conversation directly led up to the subject of religion, but pounce all of a sudden there it is and now the person has forced your to discuss it.
What you are basically getting at is unrequested information being sent to you through advertising. Many are offended by any religion that uses this approach. This is not my personal style (and assume we are the same that way) as it could be considered rude, I think if it is done gently and with kindness it is not. For example, if a Buddhists smiled at me in Hong Kong and held out a pamphlet for me to read, I would not be offended I just would not grab one. Or if someone selling a Hong Kong flat handed me a leaflet, I would not be offended. It happens every day and I am offended when they start to walk beside me and say something else when I have already declined.
A good question to ask ourselves is, ‘Why does our society take more offence at the gospel being offered than at a sale or discount of a commercial product being advertised?’ I think the poorer attitude is not in the person holding up a sign to remind others of the love of God but the great offence that people have in it. The extreme disgust that many have over some simple enthused believer just advertising what matters to them on their own free time indicates are much poorer attitude.
As far as a particular denominations in mainstream Christianity that supports this type of seemingly more aggressive form of advertising, I do not think there is one. (Of course if including less mainstream sections of Christianity, Jehovah Witnesses purposefully adopt an aggressive form of evangelism but I doubt these are the signh-olders your are thinking of). I do think it is more common among charismatic evangelicals than more historically conservative groups. This makes sense because enthusiasm and expression of feelings are more encouraged in a charismatic setting. As far as your comment that a person would not usually come to faith this way, I have never heard of anyone saying I saw a sign that said 'Jesus is Lord' and then I became a Christian. However it was a simple sign on my grandmas’ door to her kitchen with the verses of John 3:16 on it that landed into my head when I cried out to God and was saved. I knew little else about God at this time other then what I gleaned from television shows. Even the smallest advertising can carry influence in some cases.