Could Allied fleets trap Japan in the Java Sea?

Could Japan chase the British and Dutch too far into the Java Sea and find the Americans behind it?

Yes, but the Allies would still try to combine their fleets because separate forces are harder to support and easier to defeat.

The Royal Australian Navy would probably operate with the British and Dutch force, while American carriers approached from Australia. That geometry could place Japan between two Allied groups. It might also shape Australian memory by showing British ships fighting forward instead of appearing to abandon the region. Yet the same separation risks defeat in detail, so planners would still prefer to combine as much strength as possible before battle.