2 things...
1: Yes Final Cut Studio 2 and Final Cut Studio 3 will work on newer operating systems, as long as you have pre-installed Rosetta. I am running Final Cut Studio 3 on a Mavericks MacBook Pro, and it works well.
2: If you have FCP X installed, you will have to re-install FCP X after, for some reason when you try and select a different location for FCS2 or FCS 3, it will not allow this, you have to use the standard install path, this will overwrite FCP X. I just re-installed FCP X after Final Cut Studio 3.
What I noticed is that the app store picked up on the Final Cut Studio 3 install and offered updates, which I installed, once I was happy with the installed updates, and FCP 3 worked, I ran the app store and re-installed X, and both work, you cannot launch both or run both at the same time, it is either 1 or the other.
There is 1 caveat, FCP 3, will read older projects, if you have a project created in 3 and try to open it in Final Cut Studio 2, it will not work.