The protein denaturation by boiling for 10 min in SDS-loading buffer for overnight and keeping on ice for overnight will not cause degradation of proteins present in boiled sample buffer. However, before loading try to warm it and vortex to dissolve precipitate, if any.
Once the protein is added in sample buffer and boiled for 10 min, it can be kept for several days or months if stored at cold temperature.
The protein degradation may occur, if the samples are stored for a long time at room temperature. Storage of sample at room temperature for long time may cause the growth of microorganisms that can degrade the protein present in the sample.
However, it is always suggested to use the boiled protein sample for SDS-PAGE ASAP to avoid any adverse possibility.