How does time off for a serious illness affect funding and duration of PhD?
I'm at Simon Fraser University in Canada, but I've recently been dealing with this issue as I'm involved with our grad student association, so I wanted to respond to your question. If you don't change your registration status in any way, your semesters will almost certainly count against you in every way imaginable -- everyone thinks you're making progress and there is nothing to say otherwise. You should look into your university's 'on leave' policy, as that will be the formal mechanism that allows other allowances to take place. Here, leave for medical reasons will require going through your supervisor (and in turn, a faculty committee), but is essentially always granted, so I hope that works the same where you are.

Unfortunately, funding entities likely have their own, probably very specific, rules, so it's unlikely any general advice would cover them.

Ultimately, I highly recommend taking formal leave (i.e. changing your registration status), because various negative effects will likely accrue otherwise.