Generally router functions are not affected by having the wrong time as long as the time is consistent. Problems will occur is the time is being randomly reset. So if your router boots up and thinks it's 2002, it will run quite happily, pretty much forever, as long as the time doesn't suddenly change.
Also, even if it does change via NTP, leases etc will be correctly adjusted as a time reset by NTP is a normal expected event and most times are stored as offsets/differences so won't need altering anyway (a time counting down a given number of seconds will continue to count down).
- Leases are allocated based on a time difference, so as long as the time is consistent this won't be a problem
- The WAN assignment will similarly be a time difference, so shouldn't suddenly expire
- Running NTP on the router will, obviously, not work correctly is the router's time is wrong, but, if this was the case you'd have noticed it sooner
- Logs will we incorrectly timestamped, but presumably you haven't been checking these (if they exist)
- If your router has NAS features, the file timestamps may or may not be affected, depending on the exact implmentation, since often the connecting client sets the date/time on files directly
Overall, having the wrong time on the router shouldn't affect your wifi connections, but it's probably a good idea to set it correctly, ideally via an NTP setting.
A more significant problem may be if the time on your router randomly resets as this may indicate that the router has a fault.