Will these bookings update the budget automatically?

Absolutely! When using Plan, estimated flight costs prior to booking are automatically reflected in the 'Estimates' column on the Budget screen. Once you lock your budget and refresh flight data from either the Flight List or the timelinetimeline, those figures update the 'Working' column. As flights are booked—whether through Smart Capture or manual entry—the 'Actuals' section of your Budget will be updated accordingly.