I wouldn't take a 15' boat through the Hell Gate, or in the East River at all, on any regular basis. The problem is not just the currents, it is the traffic in a confined waterway, and the waves themselves. You can get 2-4' tall square standing waves reflecting up from the bottom in the East River, and that's a rough ride for a 15' boat of any kind.
If you know what you are doing, and you are very much aware of the conditions, it certainly could be done safely. But if you have to ask, no, stick to the Sound or the harbor and skip the East River entirely for now.
And even in the harbor--remember that traffic will have a hard time seeing you. If you can't get out of their way, there may be nothing they can do to avoid running you down. There's much more room in the Sound, and bays where you can have plenty of fun without the current or traffic.