No, that person could be a "martial student" or a "martial trainee" or maybe a "martialist" but, using your logic, anyone who taking a painting class would also be an "artist"
An "artist" has enough passion and commitment to devote enough time and effort (often making huge sacrifices) that take his/her chosen craft to a level not attainable by the casual dabbler.
For me, another HUGE part of being a martial artist is understanding the gift of those who preserved the knowledge. and demonstrating that appreciation through respecting their traditions and protocols.
So a child who picks up some chalk and draws their little vision of reality on the sidewalk is not an artist? At what point are they "deserving" enough to be called an artist?
That's some sanctimonious crap right there.
To echo Steve, at what point in a person's training can they be referred to as a martial artist? I don't care if someone has been training for a year, 10 yrs, or 50 yrs. If they've started walking the line of a martial artist, I'll refer to them as such.