The SC was started with this goal in mind, yes. Cristina herself reported that she felt she had gone from B2 to C2 in French thanks to it. But she started learning French at about the same age as her daughters are now, she's been in immesion situations many times and read a lot of books too. For me the best thing about the SC-scale quantity of input is that it makes you *want* to use the language. I'm not actually against speaking or writing, I just want output to come naturally. Shadowing, scriptorium, lyricstraining, LR or just listening and reading separately help a lot with that. However, as for C1/C2, according to Cavesa the latter is actually easier. If you can pass C1 with targeted preparation, you may be able to pass C2 too. The main question is still how far you are from C1/C2. It's often recommended to have a session with an experienced tutor who can tell you which exam you can reasonably expect to pass.
I didn't find the right solution from the internet.