I was traveling TXL-MIA-LAX last January.

The TXL-MIA (AA codshare with AirBeriln) was delayed so I could not take even the last flight to LAX and I had definitely to stay overnight in MIA.
My bags were checked only trough MIA.
In MIA, I got re-ticketed and re-booked for the next day. I got my boarding pass, checked my bag and one oversized item and went to sleep to the hotel.
So yes, I was allowed to check in 10+ hours before departure and the day before departure.
No issues with the oversized item but my bag arrived in California 3 days later.