Yes, you can do that. When you set up a budget, you don't specify any dates (actually, you can't). The budget is for a period. Then... when you want to view or check if you are doing OK, you click on your budget where it shows you your budgeted categories with the allocated amounts and the actual spending. Here, the date defaults to the 1st of the month, but you can change it to any date, in your case you'd start from the 23rd of the previous month.
