Yes, there is a small battery, about 3 mm across and 1 mm high, as a backup for the system timer while you are replacing the main battery (or the main battery is dead). It is supposedly rechargeable but it is never recharged (rumours are that an updated kernel enables the recharging but this did not happen in my experience), so it eventually dies after a few years.

The only negative effect is that, if you let your main battery discharge (or take it out), then the first thing the phone does the next time you switch it on is ask you to enter the current date and time.

I have been wondering about that too. Particularly the capacitor idea, but the lack of recharging put me off that. Another battery might help, as nonsuch says, but it seemed too much hassle to me to bother.