SQL is linear, so it wont start a statement until the previous has completed, there could be an issue with transactions, overlapping, or not completing in time for the next statement starts, especially if you are using NOLOCK hints on your queries, but would need to see the code in full.

I know this is going to sound daft but why not just do

DELETE FROM TheTable where week_num=10

UPDATE theTable

SET week_num=Week_num+1

Insert new week Into TheTable