The main reason why I am concerned about having only crafts in the title is that I think that Google produces results based on URL names.
URL may influence Google results, but only by a very tiny amount, if at all.
If it worked the way you were suggesting, companies selling merchandise would always name their website URL with the merchandise type, instead of the company name. But they don't.
Note that "Stack Overflow" is www.stackoverflow.com, not www.questionsaboutprogramming.com, yet it does just fine.
So, if a person interested in drawing searches "Drawing forum", will this site be on the front page of Google, or because of only crafts word in the url, Google will not show it in its top results?
They will find this site if there are questions that discuss drawing.
P.S. I know this is not a forum, but many people out there won't know any such thing initially, so they are likely to use the word forum while searching.
I think this is an assumption based on your search habits, and is likely not applicable to the general public. I expect most people would get here from searches like "what is the difference between cheap and expensive oil paints?" or "why does my ink bleed into the paper when I draw?".
Word craft does not hint drawing(arts) also.
The site isn't "Crafts". It's "Arts and Crafts Stack Exchange". Again, I believe you're placing way too much importance on a single word in the URL. That's not how search engines work. That's not how people are likely to find us.
If you specify crafts.stackexchange, people won't automatically understand that it is about drawing(arts) also.
Again, I feel you're making a broad assumption I don't necessarily agree with.
When it comes to people visiting new websites, the interaction generally is a repeating cycle of them saying "hrm... I wonder if this site has what I'm looking for?" Imagine that every couple of seconds that question goes through their head. If, at any point, the answer is "probably not", they'll likely leave. But so long as the answer is "maybe", they'll likely continue looking.
But context is everything. People aren't going to just see a URL, with no context. If you email your friends about the site, and just say "crafts.stackexchange.com", yes, they'll likely ignore you. But you're more likely to say "Hey, check out all the good information about drawing (or ceramics, or knitting, or whatever) on crafts.stackexchange.com."
Arts include drawing and painting.
"Arts", however, also includes things that aren't on topic. "Liberal arts" is a broad type of education. "The Art of War" is a famous book on warfare. "Pickup artists"... well, I won't even go there.
The point is that the word "arts" is not a magical bullet that will clearly and consistently remove all confusion about what the scope of this site is (which hasn't even been fully defined yet, anyway).