If each schedule is its own budget and has its own total, do you need to add the schedules together to give an overall total? In theory you do not, however why wouldn’t you? Adding up totals across schedules helps you to understand your budget and your development in far greater detail. It is, in my experience far easier to manage contracts at a global level across a development and know where you can and need to drill down into the costs.
This doesn’t mean you lose sight of the granular detail and disregard schedule by schedule budgeting. It just means you use all the available data to give yourself the best possible chance to succeed in the management of what may be a complicated development.
As always when it comes to anything financial, especially forecasting with budgets, the more information you can give yourself, the better prepared you are to do your job.