Scaling features by using polynomial features - python-3.x

Question

I understand the concept of polynomial regression and the use of PolynomialFeatures by sklearn.
But to get a concrete hold over the concept of using PolynomialFeature expansion, I just wanted to ask about a scenario.
Here, I want to consider a scenario of polynomial features with KNN instead of regression.
This is how we use polynomialFeatures for regression.
from sklearn.preprocessing import PolynomialFeatures
X_train, X_test, y_train, y_test = train_test_split(X_T, y_T, random_state = 0)
poly = PolynomialFeatures(degree=3)
X_T_poly = poly.fit_transform(X_T)
X_train, X_test, y_train, y_test = train_test_split(X_T_poly, y_T, random_state = 0)
fin = LinearRegression().fit(X_train, y_train)
Now, what if I do this:
from sklearn.preprocessing import PolynomialFeatures
X_train, X_test, y_train, y_test = train_test_split(X_T, y_T, random_state = 0)
poly = PolynomialFeatures(degree=3)
X_T_poly = poly.fit_transform(X_T)
X_train, X_test, y_train, y_test = train_test_split(X_T_poly, y_T, random_state = 0)
knn = KNeighborsClassifier(n_neighbors = n)
knn.fit(X_train, y_train)
In former we are doing regression (I get it. OK) and in later we are using KNN.
Does it make sense to apply KNN here and is right(in the first place)?
How are the features being transformed in case of KNN?
After going into .fit_transform() I found this:
The function has noting to do with coefficients and intercepts.
def fit_transform(self, X, y=None, **fit_params):
"""Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params
and returns a transformed version of X.
Parameters
----------
X : numpy array of shape [n_samples, n_features]
Training set.
y : numpy array of shape [n_samples]
Target values.
Returns
-------
X_new : numpy array of shape [n_samples, n_features_new]
Transformed array.
"""
# non-optimized default implementation; override when a better
# method is possible for a given clustering algorithm
if y is None:
# fit method of arity 1 (unsupervised transformation)
return self.fit(X, **fit_params).transform(X)
else:
# fit method of arity 2 (supervised transformation)
return self.fit(X, y, **fit_params).transform(X)
So is it ok to do such practice of using PolynomialFeatures with KNN as above?