I also do Edexcel and I am about to sit my c3 and c4 papers this week.
Firstly, why would you choose to do S2? There are easier options to choose.
Anyway, I mainly taught myself A2 maths and was able to do it in about 6months. This was also at the same time as juggling two other subjects. C3 and C4 are a big jump from C1 and C2. However if you put in a lot of time and work it will become easier of course.
To put this into perspective, for C2 the only identities for trig you need are
1. tanx = sinx/cosx
2. sin^2x + cos^2x = 1
However for C3 you need to know around 17-20 trig identities (although they do give you 6 in the formula booklet).
Sorry if that sounds daunting, it does at first. But once you learn it all it isn't too hard.
It would be a great idea to get started on this before year 13 starts and it'd give you a huge head start. So I advise doing as much as possible. But I couldn't imagine more than 70% of C3 being completed and learnt in thorough detail over the summer unless you chose to spend a lot of your lovely summer inside.
My advice is go for it and do as much as you can as it'll help you a lot, but don't expect to finish it all over the summer.
Hope that helps.