Alpha, my iPods are used and cared for the same way, including one connected to the stereo. So far, so good, regarding the batteries. Sgoes for my laptop PCs that are constantly plugged in.
Nevertheless, not all products like this treatment. A product I have called My Wireless Passport (hard drive) has had issues for me and others. The batteries can overcharge and swell the Li battery so much that the case pops open in worst case situations, and reduces the battery life in others. The situation was bad enough that the manufacturer redesigned the firmware of the device to drop battery to 80% max charge during long periods of overcharging, and they advise against over charging.
So, each device's batteries are unique, and it could be possible to overcharge a BT speaker battery beyond repair. One needs to monitor the situation if overheating, etc is an issue.