Can I leave my T/C plugged in to A/C when not in use?

Battery University on charging lead acid batteries.

I'd suggest to remove any standby loads when putting batteries in storage and follow published advice on proper float charging techniques. The batteries should also be monitored with a voltage meter and a hydrometer to get the most life possible out of them.

Anecdotal advice is sometimes a good indicator of what to expect but there is also a rash of bad conclusions in the mix.