sleep mode and watchdog at the same time
When you sleep the Arduino is locked up. So yes, the watchdog timer will time out and reset the Arduino.

But, since you're in sleep mode, it's not so much a "reboot" as a "wakeup".

The watchdog timer is one of the normal ways of waking up periodically to do things.  If you want to use the watchdog for its other "anti-lockup" purpose then you will have to arrange some other way of waking up before the watchdog is due to expire so you can "kick" it.

Or you disable the watchdog entirely before going to sleep so that the only wakeup source is whatever source you have configured. Then you can turn the watchdog on again when you wake up.

However that probably means that the watchdog is useless, since chances are you won't be awake for long enough periods for the watchdog to have any effect.

Sleeping and using the internal watchdog as a watchdog are pretty much mutually exclusive.  If you sleep, then the watchdog is a periodic wake-up source.