No. Scores are not automatically sent. You can send them after you receive results.
It used to be conventional wisdom that test optional was only really optional for disadvantaged students. Currently, however, both prep schools and colleges really mean optional. You don’t need to prove it would be hard to take the test.
Whether or not to submit scores might depend on the degree of difficulty of the OP’s courses so far. They did not note the level of math courses, for example.
That’s a good point, my school doesn’t offer advanced/standard maths courses until next year, so I’m not quite sure how difficult our maths classes are in comparison to other schools. I’d assume since I’m at an IB school they’d be on slightly more difficult, but I don’t know.
I suggest you prepare for the SSAT, take the test, and submit the scores if the composite is at least the 85th percentile.
Thank you, that’s what I’ll do.
And thank you to everyone who’s replied! I’m applying to Exeter, St. Paul’s, Andover, and Choate. I’m still considering Hotchkiss, not sure about that one. I realize this isn’t widening my pool that much, but I’m glad I added a few schools, and I’m looking on Niche/BS Review to find more options. I’ll be preparing for and taking the SSAT probably in December, or January, and if I get scores in the 85th percentile I’ll submit them. If anyone has tips on how I should prepare, or where I can find advice (perhaps there’s a thread?) please share. Finally, thank you so much to everyone who replied!
…may have thanked for replies a little too much there 
While there are many different approaches to writing an essay, you could talk about your gender transition - the rationale behind your decision, the challenges you had to overcome, and how the process shaped your strengths, etc.
You made the right decision to take the SSAT because your school might be foreign (pun intended) to boarding school AOs - it is hard or even impossible to evaluate the course rigor of your current program. A good SSAT or IEEE score will take the guesswork out of the equation and tick off another box.
Also, remember that applying to 5 top schools does not increase your chances by 5x. It’s all about probability. Good luck!
OP is at an IB school so AOs in the US understanding the rigor is less of an issue. The test also requires traveling to another country. Advice that OP needs to take the test is a bit misplaced under those circumstances.
If it isn’t a huge hassle, go ahead and take the SSAT, if it is a huge hassle, trust that schools really do mean optional.
I belong in the old school and believe that you should submit as much objective evidence as possible, which is why I have always advised kids to take the tests to the extent possible.
When in doubt, applicants can call or e-mail the school AOs and ask them what % of freshmen were accepted without submitting test scores. I believe most top schools would tell you-some of them even publish it in their admission stats.
I know a considerable number of new students here ( PA ) who did not submit scores. When they say test optional, they mean it. If OP has to travel to another country to take the test, imo it’s probably not worth it, and unless the score is extremely high it likely won’t matter much anyway.
OP, there are a lot of threads on here with SSAT advice. I would recommend using the search bar to find and read through some of them. This was the first one to come up when I searched, but there are many more: My SSAT is in 10 days
Good luck with everything!
Take a look at George (in PA). It’s an IB school and is very welcoming to Trans students. There are a lot of things in your profile that would suggest this could be a great fit. Also generous with FA.