Are kung fu monks and all related Hollywood stereotypes based on any actual historical connection between Buddhism and martial arts? Or is it just a fun movie concept? :)
There is a legend that Bodhidharma instructed the monks at the Shaolin Monastery in ways to increase their physical fitness. These exercises later became the Shaolon kung fu. As one of the documents involved seems to be a forgery, scholars now doubt this connection.
This is just one more good example on how Buddhism mixed with local culture, Buddhism began in India and spread through Asia, in many countries it incorporated local practices and believes just like all main religions have done, things like Martial arts, Astrology, Tantra, etc were local additions, I'm not saying this is right or wrong, good or bad, but it didn't come from the original teachings and practices.
I heard many of my relatives tell me this(I am a Indian BTW, so I assume what my relatives tell me has some degree of truth to it cause some of their ancestors might have known the correct answer to this and they passed down their wisdom to these folks) that Buddhist roam around all over the world to preach Buddhism and as required by their travel used to go to all the dangerous places where there is a high probability of them getting mugged !
So things like karate, kung fu came into being as a self-defense techniques !!
If you think about it, these Buddhists used to frequent the silk route to spread Buddhism which was also frequented by traders carrying insanely precious goods and hence attracted most muggers ! Given the fact that Buddhism just came into being during that time, these muggers couldn't tell a monk from a trader so its not tough to imagine these monks getting attacked frequently by them hoping to find silk, spices, gold or something precious ! So these monks must have invented Kung fu and Karate as a self defence technique which gradually became more than that ...
A short answer is NO. In the history of Buddhist foundations, there is nothing to do with martial arts.
By the way, these kind of monks in China are real. They have adapted and created their own way to train their minds (and bodies) by applying some "part" of Buddhist philosophy.