You'd likely see those men in New York relieve the siege at Yorktown in this scenario...
Yeah, because it's just a short drive down I-95 right?
Washington led his army out of it's positions near New York on August 19th and left Williamsburg to begin the seige at Yorktown on September 28th. It took him nearly six weeks of marching through friendly territory which also provided him with supplies to reach Yorktown. A British relief column from New York could have not made the same march in the same time, if at all.
A British column would be forced to either carry or forage for most of it's food supplies. That column would be marching through hostile territory and would be shadowed by portions of the Franco-American forces still watching New York. Unlike the Franco-American forces whose seige train was delivered by the French fleet, the British relief column would have to bring along it's artillery train for all or most of it's march. The Royal Navy will not be able to "deliver" the artillery to any point within Chesapeake Bay so the nearest delivery point to Yorktown would be somewhere along the Delaware coast near Philadelphia.
Finally, any British relief column would have to be large enough to deal with the roughly 18,000 troops in Franco-American force at Yorktown without also weakening the defenses of New York, the primary British military and naval base in the colonies.
The British did begin planning a seaborne relief column after their naval defeat in the Battle of the Chesapeake, but shelved those plans when news of Cornwallis' surrender arrived. An overland relief column was never seriously considered for the reasons I outlined and others.
If the British had taken West Point the situation hardly changes at all. They would have been able to raid further up and along the Hudson but the lines of communication with Canada would still be severed by Ticonderoga and other American forts. Supplying the West Point garrisons would be difficult as it would have to rely wholly on river transport. The Americans would still be able to cross the river whenever British ships weren't present, which is what was occurring already.
Extending the British NYC defensive perimeter as far up the Hudson as West Point may have turned out to be more of a failure than a success.
Bill