Yes. The river flows both ways all the way up to Albany and is considered an estuary. Ebb tide is almost always stronger then flood as you would expect for a river. Navigating against the current in the Hudson can cost you up to 2 1/2 knots but usually less.
Stu is correct of course about the currents being dynamic. The flood at the Battery starts before the ebb in the East River is done. 2 hours later the entire East River is flooding NE into LI Sound. And yes Sum, the current in the East River is either NE or SW. The best way to visualize this is with the current charts for NY Harbor & LI Sound that are found in the Eldridge manual (even an old copy will still inform) which show the current speeds for every hour of the flood and ebb. I couldn't find a similar reference on line but here is a link for the Eldridge:
http://www.defender.com/product.jsp?path=-1|9489|38715|803256&id=1303801
I have gone around Manhattan a few times and concur with what others have posted. Coming from Stonypoint I would stop for the night at Liberty Landing Marina:
http://www.libertylandingmarina.com/marina/rates.php If you do it before May 15th the slip rate is $2.50/ft and $4/ft afterwards. The next day head up the East River 2 hours after high tide at 'The Battery' and you will be surprised how fast you reach the LI Sound.
It is really a fun trip but I can't stress how useful the Eldridge (or equivalent) Tide & Pilot book is when planning a trip like this.
Enjoy.