No, Smart Bidding does not alter your total budget. Your overall budget is constrained by Apple, and the tool will not exceed this total budget. Note that it's possible for your daily budget to be exceeded, which is consistent with how Apple Search Ads operate, but your monthly budget will never be surpassed.
If you have further questions on MobileAction’s products or encounter any issues, feel free to contact your dedicated Customer Success Manager via your communication channels or the support team via Intercom.