No.  You are most definitely not.
(Not Irish, and not worth it.)

I'm all for everyone saying, 
"On St. Patrick's Day, everybody's Irish!"

But Budweiser's American.
Started in America.
Named after... nobody.

Shamrocks and a green bottle don't change your nationality.

They're not German,
they're not Czech,
they're not Irish.
They're American.

And they suck.

(Read the Wikipedia article about Bud to learn about the dubious origins of their name.)

Sadly, their product is brewed in other places around the world, including Dublin, but that doesn't make them Irish.