Should I pre-compute embeddings from a frozen network or are the gradients important?

Question

I'm training an AutoEncoder-like network to take a face embedding, encode it, decode it, and then I calculate the loss between the input and output embedding. The input embedding is calculated by passing an image through a pre-trained frozen network. Is there a difference between pre-computing the embeddings from the frozen network before training and computing them during training to have gradients?