When I was thinking about applying for graduate school, I asked my teacher at the time, who was Ivy-league educated, "Please be honest, does it really matter where I go to school; does anybody actually care?"
My professor smiled at me and said, "I'll put it this way: no matter where people went to school or currently teach, we all see each other at the same conferences and the same festivals. Even though their school might not be well-known or fancy, they're still doing good work."
To answer your question, I'll say it this way: I've learned as much from school as I've learned working in professional settings - the difference is in one of those environments nothing really bad happens if you goof up. Just about every "success" I've experienced has not been because of my education, but because I've hustled for every opportunity - I've created them for myself.
An educational institution does make it more likely that your "orchestral" piece will be programmed - they have concerts entirely devoted to student compositions, some of which are orchestra-themed (to give them experience of writing for large ensemble). However, a specific education does not increase your likelihood of being rejected.
As others have alluded to, it comes down to product, not just the music, but you yourself. Here are three things that actually matter:
1.) The score must look good. It's gotta be perfect, publishing-house or better quality. I judge scores for competition and also do engraving work, and any issues in the visual score reveal glaring problems in a composer's skill-set.
2.) The music must be good. Don't waste your time wondering what other people want you to write. If you're grooving on it, then the rest is out of your hands - your job at that point is to shop that piece around until it resonates with somebody. It'll eventually happen, you just gotta play the odds. That said, irrespective of content, the piece must be well-crafted. People can see a well-crafted piece of music even if it's not stylistically in their wheelhouse. (Also, as an aside, unless a group/organization has a specific concert theme, almost no-one cares about artistic style.)
3.) You have to be active. When you apply for festivals, commissions, competitions, residencies, workshops, etc, people (like me) want to see that you're really active in the music community. So if you've got regular performances, some commissions lined up, maybe some teaching or outreach, cool collaborations, active professional development (workshops / festivals), then you'll be more likely to be programmed. If you've never had a performance and you're looking to make your world-debut with an orchestral piece, good luck.
Bonus:) Just for you. You have to hustle, and you can't stop. Me personally, I get rejected by about 100 things a year, at least. I apply to so many things I don't remember what they are. (In fact, earlier this year I got an email saying that I was a finalist for a major award, but I needed to sign and return a confirmation of the score I submitted. I had no idea I applied for the award or even what piece I submitted. That's an instance where not keeping track can hurt you, or at least it did me.) Once during a phone call with a famous composer, I was shocked to find out that he knew who I was. He said, "oh yeah, I judge on a lot of things and I see you come up all the time." I hadn't ever won anything he judged, but he knew who I was because he saw I applied for (and still do) just about everything that comes up.
The point of this isn't about bragging - I don't need the ego-boost (I'm puffed enough as it is.) The point here is that nowhere in any of those stories or experiences did school or education play a determining factor. It was work, product, tenacity, and professionalism that has been and continues to be the glue of how I engage with the music community.
So, do the work, do your best work, and don't stop doing it.
Hope this helps.