Doc2Vec Unsupervised training
You should watch out for docs with more than 10000 tokens – that's an internal implementation limit of gensim, and tokens beyond the 10000th position in a single document will be ignored.
But whether you should split documents into 1000-token chunks is entirely dependent on what works best for your specific data and goals. If you have reason to consider it – perhaps you want to get back results of subdocument ranges? – then you should try it, compare the results to the alternative, and use whichever works better. There is no general answer.
I need a suggestion in unsupervised training of Doc2Vec for the 2 options I have. The scenario is I have N documents each of size greater than 3000 tokens. So now for training which alternative is better:

Training with whole document as such.
Breaking the documents into chunks of 1000 tokens and then training it.