Assuming that Congress allows it (in actuality, I don't think they will), then South Vietnam has a very good chance of surviving. American airpower plus American supplies and finance I think would change the calculation of what to do in Hanoi. IOTL, there was a debate within the Vietnamese Politburo whether to press the war, or to abide by the peace accord terms and rebuild the country. That debate obviously went the way to reneging on the peace and continuing the war.
Hanoi was operating on the assumption they had a limited window for victory before the South Vietnam Army was well enough to survive, its economy had recovered, and when their own reconstruction needed to begin. If South Vietnam was supported by large American finance and supplies, and could rely upon American bombing campaigns against the Ho Chi Minh trail and conventional North Vietnamese forces, Hanoi cannot win within their window of opportunity. Most likely, North Vietnam does not even resume the war although continues to support the Viet Cong. Instead, they will hope to restart the war in a decade or so after they "recover". Of course by then, the Soviet bloc has begun its economic collapse and there will be no war. IOTL, communist Vietnam began economic reforms in 1986 to fend off collapse.
If you say there is no American air campaign, but that US provides sufficient financial and military aid, then Hanoi may continue the war as a gamble that they can win in several years. I think South Vietnam has a better than 50/50 chance of surviving until at least 1977 or 1978 by which time North Vietnam will have to give up so they can rebuild their country. IOTL, South Vietnam's plans were based on the lack of sufficient support given by the US. This lead to several errors which resulted in the quick collapse of Saigon. ITTL, Saigon won't need to do that and can retain the correct posture. However, there is always uncertainty in war, and a major mistake on the South's part could result in a significant Communist victory.