No, it’s not. “For the cause of immorality” has nothing to do with anyone’s behaviour
after the wedding (otherwise, what’s up with the vow of “for better or for worse, until death us do part”?

“For worse” surely includes any bad behaviour on the part of the spouse.)
Rather, it refers to whether the marriage
itself was lawfully contracted - for example, that they were not brother and sister at the time of the wedding, and it is a first marriage (ie: a non-adulterous marriage) for both of them.

And more to add to your point…
NAB
Mark 10:2-9 The Pharisees approached and asked, “Is it lawful for a husband to divorce his wife?” They were testing him. He said to them in reply, “What did Moses command you?” They replied, “Moses permitted him to write a bill of divorce and dismiss her.” But Jesus told them, “Because of the hardness of your hearts he wrote you this commandment. But from the beginning of creation, ‘God made them male and female. For this reason a man shall leave his father and mother (and be joined to his wife), and the two shall become one flesh.’ So they are no longer two but one flesh. Therefore what God has joined together, no human being must separate.”
Footnotes:
[2-9] In the dialogue between Jesus and the Pharisees on the subject of divorce, Jesus declares that the law of Moses permitted divorce (Deut 24:1) only because of the hardness of your hearts (Mark 10:4-5). In citing Genesis 1:27 and 2:24 Jesus proclaims permanence to be the divine intent from the beginning concerning human marriage (Mark 10:6-8). He reaffirms this with the declaration that what God has joined together, no human being must separate (Mark 10:9). See further the notes on Matthew 5:31-32; 19:3-9.
Luke 16:18 "Everyone who divorces his wife and marries another commits adultery, and the one who marries a woman divorced from her husband commits adultery.
1 Corinthians 7:10-11To the married, however, I give this instruction (not I, but the Lord): 7 a wife should not separate from her husband --and if she does separate she must either remain single or become reconciled to her husband–and a husband should not divorce his wife.
Footnotes:
[10-11] (Not I, but the Lord): Paul reminds the married of Jesus’ principle of nonseparation (Mark 10:9). This is one of his rare specific references to the teaching of Jesus.
Matthew 5:31-32 "It was also said, ‘Whoever divorces his wife must give her a bill of divorce.’ But I say to you, whoever divorces his wife (unless the marriage is unlawful) causes her to commit adultery, and whoever marries a divorced woman commits adultery
Footnote:
[31-32] See Deut 24:1-5. The Old Testament commandment that a bill of divorce be given to the woman assumes the legitimacy of divorce itself. It is this that Jesus denies. (Unless the marriage is unlawful): this “exceptive clause,” as it is often called, occurs also in Matthew 19:9, where the Greek is slightly different. There are other sayings of Jesus about divorce that prohibit it absolutely (see Mark 10:11-12; Luke 16:18; cf 1 Cor 7:10, 11b), and most scholars agree that they represent the stand of Jesus. Matthew’s “exceptive clauses” are understood by some as a modification of the absolute prohibition.
It seems, however, that the unlawfulness that Matthew gives as a reason why a marriage must be broken refers to a situation peculiar to his community: the violation of Mosaic law forbidding marriage between persons of certain blood and/or legal relationship (Lev 18:6-18). Marriages of that sort were regarded as incest (porneia), but some rabbis allowed Gentile converts to Judaism who had contracted such marriages to remain in them. Matthew’s “exceptive clause” is against such permissiveness for Gentile converts to Christianity; cf the similar prohibition of porneia in Acts 15:20, 29. In this interpretation, the clause constitutes no exception to the absolute prohibition of divorce when the marriage is lawful.
Haydocks Catholic Bible Commentary
Ver. 9. And I say to you. It is worthy of remark, that in the parallel texts, St. Mark x. 2. and St. Luke xvi. 18. and St. Paul to Corinthians vii. 10. omit the exception of fornication; and also that St. Matthew himself omits it in the second part of the verse; and says absolutely, that he who shall marry her that is put away committeth adultery. It perhaps crept in here from chap. v. 32, where it is found in a phrase very similar to this, but which expresses a case widely different. Divorce is in no case admitted but in that of adultery. This is what Christ teaches in chap. v. 32, and to this the exception is referred, marked in the two texts. But in this very case the separated parties cannot contract a second marriage without again committing adultery, as we must infer, from a comparison of this text with the parallel texts of St. Mark and St. Luke. (Bible de Vence) — If we did not understand it in this manner, the case of the adulteress would be preferable to the case of her who should be put away without any crime of her own; as in this supposition, the former would be allowed to marry again, which the latter would not be allowed. (Tirinus) — St. Augustine is very explicit on this subject. See lib. 11. de adult conjug. chap. xxi. xxii. xxiv. — St. Jerome, in his high commendation of the noble matron, Fabiola, says of her: “that though she was the innocent party, for the unlawful act of marrying again, she did public penance.” (In Epitaph. Fabiolæ.) — This universally received doctrine of the Catholic Church was confirmed in the general council of Trent. (Session xxiv. canon 6.)