Goldsmith gives every indication that their marriage will be successful, because Kate has chosen to disguise herself to find out who the real Marlow is before marrying him, and therefore she knows his true character, and has decided that he is a man that she can spend the rest of her life with. In the same way, it is strongly indicated that Marlow becomes acquainted with Kate through her disguise and realises that there is more to her than just beauty, and finds that he is truly in love. This leads to him being willing to even risk his father's displeasure by proposing to Kate, whom he thinks is still a servingmaid:
By all that's good, I can have no happiness but what's in your power to grant me. Nor shall I ever feel repentance, but in not having seen your merits before. I will stay, even contrary to your wishes; and though you should persist to shun me, I will make my respectful assidities atone for the levity of my past conduct.
These are serious words indeed, and as Marlow progresses to kneel and propose to Kate, it is clear that they are meant to be taken seriously. Such behaviour is included by Goldsmith to definitely show that this happy ending at the end of the play is a sincere and genuine one. Kate is a character who at the very beginning of the play likes the sound of her future husband except for his supposed timidity and bashfulness. What she does through her disguise is to effectively "cure" him of this and to bring him out of his shell, making him willing to testify his love for her even before he knows her true identity. Having been willing to forsake everything in order to marry Kate, this indicates that their marriage will be successful when he actually finds out who she really is.