No.
It is true the US Coastal Command found itself with a lack of ASW assets in Dec 1941. According to uboat.net the Eastern Sea Frontier had...
However, the 50 old destroyers would not have made a significant difference. More assets would be brought in from other commands. The US's failure was more about organization and tactics than material.
Operation Paukenschlag ("Drumbeat") was initially conducted by just 5 long range U-Boats with 16 more to follow, a threat even a small but well coordinated ASW fleet could contain. Only later would shorter range U-Boats be able to operate and the numbers of U-Boats operating in US waters rose above 100.
The loaned destroyers were old, poorly maintained, WW1 surplus vessels poorly suited to submarine work. It took the British months to bring some into service. The resulting Town class destroyers were not well received by the British. For the British it was less about the destroyers, and more about opening the Anglo-American military partnership. The US would have to defend their newly leased bases on British territory allowing the British to transfer assets elsewhere.
While the US was severely lacking in modern ASW assets, the 2nd Happy Time came about because the US was slow to organize proper anti-submarine defenses. During their massive shipbuilding program they neglected dedicated ASW assets instead concentrating on fast fleet destroyers. Despite British intelligence that an attack was imminent, the US failed to prepare for the attack. This was all despite being actively involved in ASW warfare in the Atlantic for some time.
They failed to enact known successful anti-submarine tactics like convoys and blackouts and radio discipline. U-Boats could navigate using brightly lit cities, lighthouses, and civilian radio stations. Ships passing in front of brightly lit coastal cities were easy night targets.
The coordination between the US Navy and USAAF (US Army Air Force) was poor making many potential long range patrol aircraft unavailable out of inter-service spite, this was not worked out until March 1942. It wasn't until March 1942 that convoys were discussed, and it took until May to get them going.
Escort units were transferred away from Atlantic convoy duty to help coastal command, but due to the lack of coordination they often sat in port. The US was acting on the outdated assumption that convoys just concentrated targets, and that aggressive hunter-killer groups were the way to go. The British had learned the hard way this was wrong; the ocean is big and active hunting was futile. Reacting to radio reports of ships being attacked was also futile, by the time a warship was on the scene the attack was over and the U-Boat safely away.
50 more old destroyers would have just been 50 more ships to waste charging around the Atlantic.
No matter how many forces were available, convoys would have improved their effectiveness. Convoys are more difficult to spot than individual ships. At the vast scale of the ocean a convoy of many ships is as difficult to spot as one ship. With many ships concentrated into few convoys U-Boats find the ocean emptied of targets.
Some try to explain the lack of US coastal convoys on a lack of escorts, but the opposite is true. Convoys force the U-Boats to come to you. Instead of dispersing in a futile effort to find the U-Boats, convoys allow concentrating of limited ASW assets. Even a small submarine chaster is a threat to a U-Boat and would force it to dive where it's slow and blind. The limited US ASW fleet would have been better off protecting convoys than individual ships.
The sluggish American response finally produced the Tenth Fleet in May 1943. Having no ships of its own, it coordinated all Allied ASW operations, research, and intelligence.
Summary
While the US Eastern Sea Frontier command was severely lacking in ASW assets at the outbreak of the war, the 50 old destroyers were poor ASW ships. The lack of ships was initially made up for by transferring units from other commands. Instead the Second Happy Time was because the US allowed themselves to be caught flat-footed and had a sluggish response.
The US had ample lead time and vast shipyards and resources to develop and build ASW assets prior to 1942 and more than make up for 50 old destroyers. They had ASW experience from their Atlantic neutrality patrols and from the British. They had time to learn from the ongoing Battle of the Atlantic to prepare contingency plans and coordinated commands, but did not. Once engaged, the US was slow to enact basic countermeasures on their east coast such as radio discipline, blackouts, and convoys instead choosing to scatter what little assets they had in ineffective hunter-killer. It took months or years to develop a coordinated, effective coastal ASW system, a system that should have already existed when war broke out.
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