You're the CTO of a company with half a million users during a make it or break it profitability period of the next few months and you're wondering if you need to be able to login to work from home? Unless you're able to get reliable access using a neighbor's connection, or are able to be in the office within 5 minutes, then yes. You need a home connection.

By the way, TimeWarner in NYC doesn't lock you in with a contract, so you can go month to month.