Would you have fulfilled your obligation to recite a blessing if you pronounced the Name of G-d in a way that was against your custom? For example, if an Ashkenazi has the custom to say "Adonoy" and he instead says "Adonai" like (some) Sephardim, has he fulfilled his obligation?
Similarly, if he were singing a song, and he used "Adonai" instead of "Adonoy", would he be liable for using the Name in vain, G-d forbid?
This question is not limited to the two pronunciations I provided. The same question could be asked with Adoinoy, Adeinoy, Adhounoy, Adaunoy, Adhonai, etc.