It’s fine for the wood to absorb the glue; that makes it stronger throughout. Glue on the surface will give a glossy appearance or a darker shade, which is okay.
When you glue the tip, keep in mind that you shouldn’t glue down past the angle of the tip of the spike. That affects birds and stilts, and isn’t “competition-legal” kendama play as far as I know. Course, that’s only if you are affected by regulation, which you prolly aren’t.