I had to give some thought to this question, KindaScratchy, since it never occurred to me as possible that you *don't* play. 

I would say personally that anyone who is not "still learning" is in a very bad place as a musician.  Pretty much every really good musician I ever met, where I personally would say that they could really play.. Every one of them always had things they were learning, working on, developing. 

But to avoid getting overly philosophical on the point and getting instead to a hopefully meaningful answer..

I would say that you can start saying "I play the violin" as soon as you personally decide you are allowed to.  But never stop learning to play.  And if anyone disagrees with your decision, just smile and wave.  But use the wave that only takes one finger, if you catch my drift. 

I don't think that would be sad.. Some of us would have great fun even trying.  But I think building a violin might be more of a qualification for calling yourself a luthier than for calling yourself someone who plays violin.  Though it is undeniable that a better understanding of the instrument itself may be helpful to better playing in some ways.

It only counts if you could play it. Now that I would love to see

Well, if it was playable enough that you could call it an instrument, why not? 

People call fairly young kids musicians, pianists, and whatever.  Why shouldn't it count?

Personally, I consider a lot of the worry and talk over what to call someone is a bunch of elitist BS ego talk anyway.   It is kind of like worrying about if someone is a musician or not.  Even if that gets settled, somebody will start talk about what constitutes a "real" musician and then maybe a "true" musician.  Life is just too short to worry about such stuff, when there's playing to do! 

I quit worrying about such things when I was about 16.   I played, and lugged a lot of gear around with me for after-school jam sessions, but some of the kids in the school band would insist I wasn't a musician because I wasn't in the school band and didn't take music lessons.  Then the band/instrumental music teacher referred to me as a musician, and that pretty much settled that.  Later in the same year, I was playing in a band and a woman from the audience in a place we were playing was hanging around and ragging on the band a bit, since she knew most of them because they'd played there before.  She asked who I was and the bass player introduced me as the new guitarist.  She asked me if I was any good, and I started going into how I hadn't been playing very long and etc.  The bassist  took me aside and said "Man, you are in the band and this is a pay gig.  She's audience.  You don't go saying anything about how you don't play good or haven't been playing long.  Somebody asks you something like that, you should just look at them, smile, and tell them 'Some say.' and shrug and go back to setting up.  You are a professional musician now, you gotta act like it, ok?"   So I had become a professional musician and a guitarist all of a sudden.  Wow, I must have not gotten the memo. 

What my point is, is that it doesn't really matter except maybe as it matters for your own attitude and morale.  If saying "I play violin" feels better to you than "I'm learning to play violin", then do it.  For that matter, if calling yourself a violinist or a fiddler encourages you to play better or more because maybe it makes you feel more committed, then take that "title" too.  If anyone gives you any trouble over it, you have to stop and think if they sign your paycheck or are the person who hands you money at the end of a gig.  If so, then you may wish to consider their feedback.  If not, then they have a problem.. Which is not your problem.  To heck with them.  Life is too short to worry about such things.