Is it appropriate to train W2V model on entire corpus?
The answer to most questions like these in NLP is "try both" :-) 
Contamination of test vs train data is not relevant or a problem in generating word vectors. That is a relevant issue in the model you use the vectors with. I found performance to be better with whole corpus vectors in my use cases.
Word vectors improve in quality with more data. If you don't use test corpus, you will need to have a method for initializing out-of-vocabulary vectors and understanding the impact they may have on your model performance.
I have a corpus of free text medical narratives, for which I am going to use for a classification task, right now for about 4200 records. 
To begin, I wish to create word embeddings using w2v, but I have a question about a train-test split for this task. 
When I train the w2v model, is it appropriate to use all of the data for the model creation? Or should I only use the train data for creating the model? 
Really, my question sort of comes down to: do I take the whole dataset, create the w2v model, transform the narratives with the model, and then split, or should I split, create w2v, and then transform the two sets independently?
Thanks!
EDIT
I found an internal project at my place of work which was built by a vendor; they create the split, and create the the w2v model on ONLY the train data, then transform the two sets independently in different jobs; so it's the latter of the two options that I specified above. This is what I thought would be the case, as I wouldn't want to contaminate the w2v model on any of the test data.