You really shouldn't, they need a full nights sleep just like we do. If you're very careful you can take them out and have some sleeping cuddle time, but for the most part handling time should be confined to daytime hours.
BTW, they need about 14 hours of daylight... Are your lights coming on at 6:30 am?
It wouldn't hurt him, it would just be rude to wake him up in the middle of the night... Some of them get rather grumpy if they don't get their beauty sleep!
And 12 hour of light is sufficient, especially during winter, so if your lights come on at 8:30 that would be fine.