Probably not
SB8 section 171.209 which creates the "undue burden" defense, sharply limits it.
It is available only when
the United States Supreme Court holds that the courts of this state must confer standing on that defendant to assert the third-party rights of women seeking an abortion (section 209 (a)(1))
or
the defendant has standing to assert the rights of women seeking an abortion under the tests for third-party standing established by the United States Supreme Court (section 209 (a)(2))
If and only if one of (a)(1) or (a)(2) is true, then under 209(b) a defense may be asserted if
the defendant demonstrates that the relief sought by the claimant will impose an undue burden on that woman or that group of women seeking an abortion.
Subsection (c) further limits the defense, requiring a defendant to prove that an award of damages will prevent (under (c)(1)) or "place a substantial obstacle in the path of" (under (c)(2)) a woman or group of women seeking abortion.
Subsections (d) and (e) further limit the defense.
Even assuming that the standing issues in 209(a) are resolved in favor of the defendant, I don't think a contract between the defendant and a patient requiring the patient to reimburse the provider for any damages under SB8 would meet 209(c). Since the law does not require such a contract, I think a court would likely regard this as a self-imposed burden, or a choice by the provider, but not a burden imposed by the award of damages. But this is a novel, untested section of a novel, untested law.
It seems clear (to me at least) that the intent was to have section 209 be just enough of a defense to make it harder to rule SB8 unconstitutional, but not to be a practical defense in any real case. But ther is no telling what arguments might be made if a defendant raises 209(b), or how a court would rule.
The fact patter that 209(b) seems designed for is an argument that a damage award would force a provider to cease operations, thus placing an undue burden if there are no other providers open and willing to act. Even so, such a defense is only available if the standing issues in 209(a) are resolved in favor of the defendant.
