Yes. I imagine conversation would be really clear from an unplugged phone.Perhaps she thought if the phone wasn't plugged in, the call wouldn't be recorded and June and Neville wouldn't know she'd made the call.
D'oh,it would have depended where the points were in which to plug the phone in

Did you know where they were situated ?
I would have imagined that Sheila wanted to have a conversation free from being interrupted or cut-off whether she was phoning Christine or any of her friends,as well as not disturbing anyone in the household. Besides it being an easier one to dial and use.
Why would Sheila have been bothered about it having been " recorded ?". The only time you could ring Canada in peace is when it's our night-time anyway 5 to 8 hours behind us depending which state. The children and June were in bed.Neville would have been walking the dogs and Sheila probably couldn't sleep.