I do. And 9 out of 10 mornings my phone is dead and requires a hard boot. At least it's charged though.
When your phone reaches full charge, the LED will first do a slow blink, then turn off almost entirely - unless you use a nightstand app or the NFC charging Weather and Calendar app. If the screen is on, it blinks a little faster, and won't turn off. This is to show that it is still charging the phone.
I do, with absolutely no negative consequences at all.
...that ive noticed.
I charge mine wirelessly every night. And I have wireless charger at work I leave it on half the time.
Occasionally it seems to get a little warmer than expected, but overall its an awesome/easy feature!