Yes they would still have been an effective tactic against a cavalry charge that was run home against infantry that was still fighting.

But there were vanishingly few instances where a charge like that was ever contemplated, and next to no place in the American Military Tradition for shock cavalry, especially heavy cavalry.

American cavalry units from before the Revolution to 1861 were almost exclusively mounted infantry or Dragoons. Meant to marry the mobility offered by being mounted, but still meant mostly to fight as light infantry. Or against other cavalry or broken infantry with a sabre. Or in extended raids behind the front disrupting the rear area and attempting to damage the war economy of either side. And commanders like Forrest, Sheridan, Wheeler, etc on both sides were not trying to do anything radically different.

There was little money for the expensive heavy cavalry found in European armies, and the heavily forested, broken ground of many American battlefields in the East limited opportunities for such massed application of shock cavalry. To say nothing of the expenses involved in acquiring the large warhorses needed by say the Cuirassiers. While the needs of the Army to garrison and patrol the Western forts and the Indian Wars, meant mounted light infantry was the way to go, and how the US Cavalry was mostly equipped come 1861(though you do see the idea of Lancers pop up here and there, including in volunteer units in the ACW).

So during the war the cavalry on both sides played very similar roles, scouting and denying the other sides reconnaissance, securing flanks and lines of communication, attempting to run down the enemy when broken, and trying to stop the other side from doing it to them. There is a strong argument that this lack of heavy cavalry contributed to so many of the battles of the war being decisive tactically, but rarely resulting in the destruction of either army, there wasnt the ability to follow up with the killing blow.

There were opportunities for traditional charges though. Stuart notably got a small one off at the end of 1st Bull Run, but other times indecision or the obvious risk involved prevented it. McClellan for example kept Pleasanton's fresh and concentrated Cavalry Division in reserve with Syke's Regulars directly across from the depleted Confederate center for most of the afternoon at Antietam.