I cannot speak for Beijing but you can get a license in Nanjing with a L visa as long as you are in China for more the 3 months. Most L visa's require you to at least leave and come back every 90 days but there are exceptions. I am married to a lovely local Chinese gal and it was much easier for me to go with a L visa that covers spouses. My visa is good for a year at a time and my wife simply goes down to the police station once a year to get it renewed, hence the reason I changed to this visa. I got my license with this L visa! Again, the key here in Nanjing at least is you have to be able to stay more than 90 days in a row. All this being said, I know for a fact, I was the first foreigner in Nanjing to get a license with an L visa. It was an 2 week affair with my wife finally going postal before getting to someone who understood how to do something different. At several points, we were told I could not get the license but she is very stubborn and persevered until I got the license. I only bore you with all this because I suspect you can find a way to get it done one way or the other once you are in China and face to face.