So not to get too pedantic here but would you consider someone who studies science and is really interested in science to be a scientist, or do you actually have to have some depth of knowledge in this field to be a scientist? If it's the latter, then it's not just about studying science but actually acquiring scientific knowledge, understanding how that knowledge is gained, etc., that is necessary to being a scientist. I imagine it is theoretical possible that that knowledge could be acquired without some sort of formal instruction (even if that is self-instruction), but it's tough to see how it can be acquired that way in practice.
So, at least two two questions here relevant to philosophy and philosophers end up being: (1) Who counts as a philosopher?, and (2) Where does studying philosophy lead you?
On (1), if we grant that there are many philosophers who lack formal degrees in philosophy (and this seems right to me), then we're looking to identify a philosopher as EITHER someone who has some sort of theoretical knowledge of the world, knowledge that is different from the type of theoretical knowledge associated with scientists, OR someone who approaches questions about the world from a certain methodological framework (OR both, I suppose). I go back and forth on this. Right now I'm leaning to the OR in that either or, but it wouldn't take much to push me back to a both.
As for (2), I can talk about where studying philosophy has led me, but it's tough to generalize from that. All of my students tell vastly different stories about where philosophy has led them, and usually all of those stories point back to what they value in life and why. So, for more, the more I study philosophy, the more I want to take my golf hobby seriously. For me, the more I studied philosophy, the more I realized how much of the world around us is complete and total bullshit and built on bullshit. The vast majority of accomplishments and achievements are conferred on us either because we've befriended the right people, said the right things, or paid the appropriate amount of money to get them. The nice thing about golf is that I'm in complete control of the equipment I buy, I can control my body, the ball isn't moving, there's no one playing defense, and while sometimes you can get really bad breaks (Tiger at the 2013 Masters comes to mind immediately), there's no bullshit. You know when you play well; you know when you play badly; you know when you're getting better. I encourage all of my students to have hobbies like this or otherwise participate in activities like this.
If everyone had this same sort of reaction to (2), where studying philosophy led them to be more reflective about their lives, what they value, and why, then it certainly seems like everyone would be better off if they spent some time thinking philosophically.