What is the conditioner you have - and how old is it?
I use fairly new conditioners and regard them as being entirely safe - they trickle charge the battery and, assuming the battery is in good condition, use very little power.
I would not leave a 'fast charger' (for example) connected up for long - but a modern conditioner is fine in my view. I have a car in my barn that's been happily sipping the juice for over a month.
