Active learning on image classification model
Yes, that is possible. In transfer learning you have at least three options to handle transferred weights:


Freeze transferred weights
Retrain transferred weights from scratch
Fine tune transferred weights (further training but not from scratch)


The 3rd one is what you intend to do. And of course different options can be applied to different layers. Also see this paper:


  The usual transfer learning approach is to train a base network and then copy its first n layers to
  the first n layers of a target network. The remaining layers of the target network are then randomly
  initialized and trained toward the target task. One can choose to backpropagate the errors from
  the new task into the base (copied) features to fine-tune them to the new task, or the transferred
  feature layers can be left frozen, meaning that they do not change during training on the new task.
  The choice of whether or not to fine-tune the first n layers of the target network depends on the
  size of the target dataset and the number of parameters in the first n layers. If the target dataset is
  small and the number of parameters is large, fine-tuning may result in overfitting, so the features
  are often left frozen. On the other hand, if the target dataset is large or the number of parameters is
  small, so that overfitting is not a problem, then the base features can be fine-tuned to the new task
  to improve performance. Of course, if the target dataset is very large, there would be little need to
  transfer because the lower level filters could just be learned from scratch on the target dataset. 


I have marked the sentence addressing your question bold.