No problem for batteries, one of the features of the Tender is it's a slow charge. Actually easier on the battery.
Tenders were designed with long term use in mind. As such they're set up to be connected and left. They have an SAE connector that plugs into a pigtail designed to be left on the bike, lawn mower, whatever. They do come with a pigtail with clamps... the full size BT has a bit of a short connector... any time I used it on my truck I had to sit the BT on top of the radiator with the hood open. May not be an issue with a car. My BT Jr. has a longer connecting cord, probably due to it being designed to plug right into an outlet.
I suppose if you know you're dealing with a vehicle that you've had previous problems a BT would be a good idea. Possibly also a safeguard against unexpected problems. Be aware BTs changed a number of years ago in order for compatibility with Glass Mat batteries. The current offering is a Battery Tender Plus. If it doesn't say "Plus" it's real old stock and I'd avoid it.
TL