As spelled out in the above article, there is no regulatory requirement that an A&P get the factory training, but all A&P's are prohibited from doing any work or process that they have no prior experience doing. This is in FAR part 65.
So an A&P with extensive GA experience can do just about anything on any GA airplane but if he gets hired by an airline, he has to work under the supervision of another mechanic until he gets the exposure/experience to any specific work that he does.
Same goes for an A&P that has never worked on or had any training on the Rotax.
I highly recommend the training, whether it be an A&P or an E-LSA builder/owner.