Nope. 343i and even Microsoft said it themselves, no Split Screen whatsoever.
Here's a tweet from Josh Holmes:
https://twitter.com/JoshingtonState/status/615282749436358656
and here is an article stating Microsoft confirmed no split screen:
http://arstechnica.com/gaming/2015/06/halo-5-listing-dev-statement-point-to-end-of-series-local-multiplayer/
(Its near the end of the article)