Yes. Once you start career mode nothing can be changed, you'll have to restart.
Things can be changed, but it's a bit more complex.
The files that the game calls can be changed. That is, you can change team badges, what images are used for the sponsors etc. What you can't do is change a team so they use different badges, sponsors and such.
For examples, for badge packs, if you already have the right logos set for the teams as in the badge pack, it'll be fine. If however you're using different logos to that badge pack it can create issues. For example, the get best early on had the Melbourne Stars and Middlesex using the same default badge, while the badge packs (needing different ones for each) need to pick one or the other to use that default badge to replace.
The same goes for sponsors and such, you can change the sponsors, but it's just replacing one image with another.[DOUBLEPOST=1410343751][/DOUBLEPOST]
But if I install the mods, will the career mode progress as normal - without mods - or will the save file essentially be corrupted/unplayable?
It's recommended you start a new career, but it won't be corrupted as it only changes the image files. You might get some odd effects, and you won't be able to do the kits. It won't change the gameplay or career direction at all.
