No - your ancestor, James Alexander, who m. Kitty Walker is not the same James Alexander as my ancestor. There is an awfully lot of erroneous material posted to the web about your James & Kitty - so you need to be careful. I do know of one researcher who has been very careful about her work who I can put you in touch with. I don't know if she has identified the parents of James who m. Kitty.
If you are interested, you can go to message # 7582 on this Alexander Forum and see the Bible record that I have posted that belongs to my line. My James was b. 1749 (much before yours) and had no sons named James.
I wish you luck. It's not easy to sort out the Alexanders!