Can I plug models like Linear Regression into a CNN feature map result?
What you're explaining is basically almost every CNN model where you basically have a fully connected layer at the end of the convolutions and that is equivalent to having a linear/logistic regression at the end (given there's only one output)

The only difference between all of those is whether there's an activation function or not, and if you are trying to build a classifier then you would definitely want an activation function to map the output values to a probability value between 0 and 1.

Example:



That "Fully Connected" layer is just basically a Linear/Logistic regression (10 of them actually since we have 10 outputs in this example) and a softmax applied to the output values to scale them all between 0/1 and ensure the sum is exactly 1.