Would Nelson have been sent to fight the United States?

If Nelson had survived Trafalgar, would Britain have deployed him against the United States?

Probably not. Britain needed competent strategic station command, which it already had, rather than a famous battle-fleet commander for an enemy with no comparable battle fleet.

Nelson's specialty would have been unnecessary against a navy with no battle fleet for him to break. The theater instead required blockade, coastal operations, reinforcement management, and strategic station command. Britain already had Alexander Cochrane and other capable commanders available for that work. Prestige alone would not have made Nelson a better fit for the mission.