Robot budget, yes. You need to fill out an official Bill of Materials that documents all the materials used on your robot and their cost. This documents that you're in compliance with the $3500 maximum robot budget.
Team budget, no. There is no general requirement that you submit your team's budget to FIRST. This MAY be a requirement of a grant you're receiving, however. Talk with the organization that's providing you the grant to find out, though that information should be contained in whatever agreement you signed to receive your grant money.
Having your team budget information CAN be useful, however. Both from obvious budgeting standpoint and for getting awards. The
Kleiner, Perkins, Caufield & Byers Entrepreneurship Award requires that you have a formal business plan available for judges to review in the Pits. A budget is obviously a very important part of a business plan. It's also useful in some small part for Chairman's to show that you have a focus on creating a sustainable program that will be making a long term difference.