I doubt that the Japanese could win. At their strongest they had barely reached parity in numbers of troops on the island and had a deficency in firepower. The naval war off shore was going to eventually go against them no matter how well they did in individual actions as the US simply had too much of a superiority in numbers and ability to replace losses.
In the air the same situation holds true. So long as New Caledonia and Esprito Santo remain in US hands the US could continue to funnel in new aircraft and pilots to the island. All the US had to do is continue to force losses equal or greater than their own on the Japanese to eventually win the air war; and they were doing this right from the start.
Disease and privation were far more severe for the Japanese than the US at every point in the campaign. The US had far more engineering assets on the island to support their operations than the Japanese. With Tulagi harbor the US could also run in fast destroyer transports to deliver supplies regularly. The US was also flying in critical supplies as they held the air field. Certainly, the Japanese could be annoying but they lacked the resources to push the US off the island and had no way of delivering them.
To put the 2nd Division ashore they Japanese beached their freighters, losing all of them in the process. This was something they could ill-afford to do given their already critical levels of shipping and inability to replace it.