I’m not sure I understood 100% your question but I think the language word2idx/ embedding mapping should not change if you want to make use of the knowledge contained in your word embeddings.
Having words map to a different word vector space is like initializing the embeddings randomly. Your model will probably converge if you allow the gradients to propagate to the embeddings and it will move the word to a vector space that makes sense for the problem you are solving but you are not taking advantage of any information the word embedding has to offer.