Are budgets useful in project implementation? How?

it sure is! budget is one of the three pillars of any implementation (MONEY, QUALITY,TIME) and in this day and time..
Money (budget) is the main driving factor as without proper and reliable budget planning and money flow you will not be able to provide the needed resources for the project.
furthermore, allocated budget can effect the scope and duration of the project as you cannot compromise quality of deliverable.

 yes by estimate  cost &determine budget   control cost

Budget is usefull for non forecast problems in Implementions.

depends on project , and field of project this budget can increase .