Ask an expert in your field that you have never met to write a reference letter?
If you feel that A is sufficiently familiar with your work and your expertise and can comment upon those responsibly, then it is not inappropriate to ask him for a reference letter. 

Your perception of your relationship maybe, however, different from his. And if that is the case he will probably politely turn you down (he is too busy, he does not feel comfortable doing it, etc.) in which case don't take it personally and don't hold it against him, and certainly don't force the matter. Having a weak letter at times is worse than not having one at all. 

If the request was made to a complete stranger, it is possible that person may develop a bad impression due to this request out of the blue. But since you have been in correspondence with A, the worst that can happen really is that he would say 'no'.

To put in a personal perspective:


I have had an experience where an expert in the field, who has read some of my papers, and who has invited me for seminars (and hence whom I have personally met), turn down a request for a reference letter because he feel he is not in a position to write me an extremely strong letter. 
I have had also an experience where an expert in the field agreed to write me a reference letter based on having read some of my papers and having conversed with some of my co-authors. We only had e-mail and Skype discussions after he agreed to write the letter and want to find out more about me and my interests.