I don't mean that it was literally named for the dropdown, just that generally Helvetica was the cause and Arial was the effect. From what I know, it goes back earlier to when Monotype was providing fonts for IBM printers.
From what I know, Monotype was responsible for the name Arial (although IBM called the family Sonoran Sans Serif.) But, even at that point, the intent was to create something that would stand in for Helvetica.
I don't know that the name was selected deliberately to be ahead of Helvetica. But, it's not unheard of in branding to put your product ahead of or near the competition alphabetically. (It was especially important then because people were manually looking up things in phone books and libraries.) I wouldn't be surprised to hear that aspect was considered during naming.
From what I know, Monotype was responsible for the name Arial (although IBM called the family Sonoran Sans Serif.) But, even at that point, the intent was to create something that would stand in for Helvetica.
I don't know that the name was selected deliberately to be ahead of Helvetica. But, it's not unheard of in branding to put your product ahead of or near the competition alphabetically. (It was especially important then because people were manually looking up things in phone books and libraries.) I wouldn't be surprised to hear that aspect was considered during naming.