Diving is a pretty safe sport and not hard to learn, especially when you have the passion and urge to explore underwater. Aspergers itself is definitely not a problem for diving. The sorts of problems people could have that might make it hard are - asthma; ear problems; bleeding problems or certain medications; panic attacks.
Actually it could be a good activity for us with AS if we like to escape people. Personally I have done 30 dives and found many of them boring, unless they were in a truly magnificent reef etc. I also find that diving takes up a huge part of a day and it's just not worth it for me, so I haven' done it for about 5 years. t never wanted to dive - I did it for my partner.
RE learning - You wouldn't have to tell them you have AS, BUT if you find that at other times your teachers or tutors don't understand your learning style or how you interact with others, you might have to help the instructor understand your different needs. Most people don't know what AS is so rather than just stating your diagnosis, you could tell them exactly how you prefer to learn and socialise.
RE "Independent diver" - you always have to go with a "buddy"; you will never be "independent" under the water, unless you become extremely advanced. So, get used to the idea that you must take a friend, or meet someone at the diving shop/school and work with them.