No it didn't. Another pilot may have tried to make it to Teterboro (which they had a visual on). Sullenberger knew from his gliding experience that his Airbus would not make it, leaving the tricky water-landing as the only option.
Yes, it was only a few seconds, but the skills Sully had as a glider pilot paid off.....huge.
But Sully did first say he was going to turn around and go back to LaGuardia (clearly impossible) and then subsequently inquired about the Teterboro option (also clearly impossible). With a couple of minutes to think through the available data, and given his gliding knowledge, he certainly could have figured out that both these options were absolute physical impossibilities. But he just didn’t have time to apply the knowledge. I think when he finally realized that the “where” decision was being made for him — probably when he saw the surface of the Hudson right in front of him, right where the runway should be on a normal landing — he instantly concentrated on the landing angle, and that made all the difference between 100% survivors and 100% fatalities. Honestly, before that, I think he was having some of the same trouble the TRACON controller was having, accepting the reality that the only place this plane was going to go down was in the Hudson. If you’d showed him a video of an identical flight, before this incident ever happened, along with all the data that was available to him in the cockpit, I’m sure he could have said within 15-20 seconds of the bird strike that, absent a miraculous engine restart, the only option was the Hudson, and that no time should be wasted thinking about any other option.