From my experience they do allow it with a permit. You will probably need to get a post installed in front of the dryer. This is to prevent a car from hitting the dryer and breaking the gas line. I hope that helped you.
It is alway6s best to ask the Building and Safety department first and to get a permit. It won't cost much but it is a bit of a hassle.
There are several offices for the LA Building and Safety, here is their web site to find out which one is closest to you. http://ladbs.org/LADBSWeb/public-home.jsf
You can try calling 1-213-473-3231 however, in my experience it takes a long time to get through all the automation.
There is no problem getting a permit to do plumbing into your garage for a washer and dryer... as long as the space allows it.
You can go to the department of building and safety and get the information over the counter. They are very helpful... make sure you have a rough drawing of what the garage looks like and the dimensions.
Just a sketch.