That is really cool! But I’d bet they don’t have enough of them. Not too long ago (2 to 4 years?) they were trucking it out to barges.
They truck it right over the river, and dump it in.
A bigger problem for NYC with this storm is that we're supposed to get some very cold temperatures for a while afterward. This means snow won't melt very soon, and one of the top priorities after the streets are plowed is to have fire hydrants dug out of snowdrifts. That usually takes several days under the best conditions.