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 possibility is that Umbridge, despite her cruel nature, sees some potential in Harry for her own gain. Maybe she tries to mold him into a perfect little wizard according to her strict and often wrong ideas. She could isolate Harry from his friends and force him to follow her rules blindly, which would create a lot of internal conflict for Harry as he tries to resist her brainwashing while living under her roof.
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.
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.
She would probably be outraged. Umbridge is a strict and narrow - minded character in the original series. Fanfics often deviate from the 'proper' version of events she might think, and she'd likely see it as a distortion of the wizarding world she believes she upholds.
In the context of the original Harry Potter story, it seems quite abnormal as Umbridge is a very unlikable character to Harry. But in the world of fanfic, anything can happen. Fanfic allows for different interpretations and character developments, so while it's not normal in the traditional sense, it's possible within the creative space of fan - created stories.
Another idea is a time - travel fanfiction. Harry goes back in time and has to deal with Umbridge when she was a student. He tries to change her path so that she doesn't become the horrible person she is in his time. This could involve him befriending her and showing her the value of kindness and freedom.
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.