Yes. Budget limits are owner-set ceilings like any other limit in Heidi Control: agents and jobs stop, gracefully and visibly, before crossing them. No surprise bills, by architecture rather than by promise.
Spend is just another resource under the limits system that governs everything agents do, so the same guarantees apply: caps are hard, approaching them is visible, and hitting one produces a clear signal, not silent failure.
In practice teams set a comfortable monthly ceiling, watch the real number come in far under it, and adjust with data instead of anxiety.