It's highly inappropriate. The relationship between Umbridge and Harry Potter is one of oppressor and oppressed in the original story. Adding such a violent and inappropriate act like spanking in a fanfic not only distorts the characters' relationship but also may have a negative impact on fans, especially younger fans who look up to the series for positive values and role models.
One negative impact is that it distorts the characters. Umbridge is already a disliked character, but this would make her seem even more malicious in an inappropriate way. And for Harry, it puts him in a demeaning and victimized position in a very improper way.
One possible consequence could be that she gets fired from her position. If Harry manages to expose her actions, the wizarding school or the Ministry of Magic might not tolerate such blatant abuse of power and take disciplinary action against her.
Another way Harry could respond is with a sense of shock and disbelief at first. Given that Umbridge is supposed to be in a position of authority, Harry might be momentarily stunned that she would go to such lengths. However, his Gryffindor courage would soon kick in, and he would likely start to resist, perhaps by using his magic in creative ways to protect himself or to disarm Umbridge, all while trying to uphold the values of the wizarding world that oppose such cruel and unjust treatment.
Fred and George Weasley are also favorites. Their mischievous nature can be amplified in fanfictions. They could create new and even more spectacular magical pranks specifically aimed at Umbridge, like turning her office into a never - ending maze of trick stairs and hidden rooms filled with various magical creatures that drive her crazy.
The development of their relationship in Harry and Umbridge lemon fanfiction can be quite diverse. It could be that Umbridge, in an attempt to control Harry more closely, gets drawn into his world in a way she didn't expect. Harry, on the other hand, might start to see through her tough exterior and find some vulnerability in her. This discovery could lead to a series of exchanges between them, some filled with tension, some with a strange sort of understanding, and over time, this shapes their relationship in the fanfiction.
Harry Potter would surely interact with her. Given their history of animosity, he would be one of the first to notice and oppose her new 'dark lady' ways. He would try to protect Hogwarts and his friends from her schemes.
She's often portrayed as extremely cruel. She uses her position of power at Hogwarts to make Harry's life miserable. For example, she might give him excessive detentions with the blood - quill, just like in the original books. And she'll try to isolate him from his friends and undermine his credibility among the students and teachers.