Travel outside UK between two jobs

I am currently holding a Tier 2 general visa. If my current contract ends at the end of October, and the new job starts at the beginning of December (which will be on the CoS), assuming I will get the new BRP before November, can I travel outside UK for about four weeks in November?
Is there any impact on the future ILR applocation?
Do I need to provide any proof for this absence when apply for ILR? (I know normal paid annual leave should be addressed on the employer letter when apply)

Many thanks in advance for help!

Anyone can help?

Thanks!