I have broken screen. Can I root my phone only with downloading mode and recovering mode?

I want to recover my data from my Samsung S Duos. I have broken screen, so I can't do anything, even unlock (because I have a password to enter the phone). I tried to install CWM and connect with ADB, but USB debugging isn't turn on, so I can't connect with ADB at all. Is there some way to root my phone via recovering mode (with CWM) so I can turn on USB debugging and work with ADB? Maybe there is some easier way to recover my data? I thought e.g. about connecting keyboard to my phone, so I can unlock it and normally connect via USB, but my phone doesn't support OTG :/ any ideas?