Speaking from experience as an aphantasic person, I think it is definitely possible to test objectively. For instance certain IQ tests will test the subject's ability to identify what a pictured object would look like if it were rotated in a certain way.

I have taken just such a test where spatial rotations, IIRC including multi-step ones, were a component, and I scored close to 99th percentile on every section except that one... where I scored 1st percentile. If that's not a strong sign of aphantasia I don't know what is!