(a) The addition of territory annexed under § 451.551, or approved under § 451.552 or 451.553, does not take effect if, before the effective date of the addition under Subsection (b), the board of the authority gives written notice to the governing body of the municipality that added new territory to the authority by virtue of annexation, or to the governing body of the municipality or the commissioners court of the county that held the election, that the addition would create a financial hardship on the authority because:
(1) the territory to be added is not contiguous to the territory of the existing authority; or
(2) the addition of the territory would impair the imposition of the sales and use tax authorized by this chapter.
(b) In the absence of a notice under Subsection (a), the addition of territory takes effect on the 31st day after the date of the:
(1) municipal ordinance, if annexed by a municipality under § 451.551; or
(2) election, if approved under § 451.552 or 451.553.