Given Japan's situation and the nature of naval warfare in the Pacific, of which the Japanese were now painfully aware, there is no reason they shouldn't have gone forward with their reinforcement attempt. The ships involved were of little value against the 5th Fleet and carriers. Their absence from the Marianas operation would have made little or no difference.
However, if the Japanese were able to land say, another reinforced regiment on Biak, disrupt the US landings and contest the island for say, another three or four months it would have been a major setback to the US planning for the Philippines invasion.
Yes, the US likely would have beefed up their efforts there. Yes, the US Navy could have reinforced the area too to prevent more reinforcements.
But, all of this is a distraction that keeps the US from moving forward. Think about the overall campaign. What if the Japanese did this and set US operations back say four months? This means the Soviets invade Manchuria in 1945 before nuclear weapons are dropped or, that the weapons drops occur earlier into the US bombing campaign.