Japan, the Great White Fleet, and the Philippines

Would Japanese refusal to admit the Great White Fleet make war likely if the fleet continued to the Philippines?

Not by itself. The Philippines were American territory, and Japan would probably turn to Britain for support rather than attack solely because the fleet was present.

In this counterfactual, Japan sees the Great White Fleet as another threatening visit like Commodore Perry's and refuses entry to Japanese waters. The fleet can still proceed to the Philippines because those islands are American territory. Its presence there alone gives Japan little justification for hostilities. Japan would immediately seek British backing, and war remains unlikely unless another intervention escalates the dispute. If fighting developed, Britain could cut coal supplies to the American and Japanese fleets and press them toward peace.