Can anyone become an anime or manga artist?

Its possible. Since Shounen Jump has a Japan-born root, you'll have to know how to speak and understand Japanese. The chances are not high of getting into Shounen Jump, since its extremely popular and seeks great artists with great stories to compliment their art. Besides Shounen Jump, there's also other manga publishing anthologies.

Answer:

First you need to have a story in mind. If you can draw, then go ahead, if you can't, you must find an artist for your manga. If you are fluent at Japanese, go ahead, if you aren't, find someone that can translate your manga to japanese. Then I don't know, you must travel to Japan or find some way like send e-mails to Shonen Jump. If they accept your manga, you have acomplished your dream.