No, this is NOT the case.
Each protein-antibody pair may require slightly modified binding and detection conditions. The variations may for example be a membrane with another pore size and physical properties (nitrocellulose or PVDF) as well as different blockers, incubation times and primary antibody dilutions. Some antibodies may work better in TBS-T buffer, others with PBS-T.
These issues are disussed in Agrisera Western blot guide, which we recommend you to keep in your lab!
Western Blot Guide