Hi, junior in high school here and I haven’t taken a real SAT yet. However, I got an 1170/1520 on the PSAT this school year without ever studying in my life (and skipping a ton of questions because of lack of time). I’m signing up to take an SAT prep course in a week or so to prepare. It’s 25 hours of class and it includes 3 practice exams. I will also be doing exam club most weekends (you take a psat at the location and get your scores immediately). Can I get to a 1400??
Yes.
Yes, just do not rely solely on the prep course. Do a lot of prep on your own. But you definitely can, if you are willing to put in the effort 
In addition to the course, a tutor can also be helpful. However, it is probably more economical to do the course first.
I think there is a good chance that you can at least get close, and you might very well get to 1400. SAT preparation really does help quite a bit.
Ok, I plan on doing preparation on my own as well
Ok, I plan on doing preparation on my own as well
If I don’t improve as much as I want to I’ll try to get a tutor