I'm far from an expert or even intermediate in Japanese, but I think not. The names of the kana are just their sounds. A sketch in Azumanga Daioh comes to mind

I'm far from an expert or even intermediate in Japanese, but I think not. The names of the kana are just their sounds. A sketch in Azumanga Daioh comes to mind, where one girl is talking about the character じ ("ji"), and another girl thinks she's talking about hemhorroids, 痔 ("ji").