https://www.mayoclinic.org/diseases-conditions/conjoined-twins/symptoms-causes/syc-20353910#:~:text=Conjoined%20twins%20may%20be%20joined,hearts%20but%20share%20other%20organs.

I think it would depend on three factors: the type of conjoining, the type of drug, and thirdly, the dose but yes, in theory, both people could feel the effect of drugs.

Thoracopagus (being joined in the chest) is the most common type of conjoined twins and they typically have a shared heart and liver. As their circulatory system (heart) and waste disposal system (liver) are connected, it stands to reason that a significant dose that is being metabolized by one twin will also affect the other due to the connected systems though likely at different rates. Something like alcohol for example, taken orally, should in theory, affect both twins but inebriate the ingesting twin more heavily as the alcohol is being absorbed through that twin's mouth and stomach and should reach the ingesting twin's brain faster.

Rachipagus (being connected along the spine) is a rare type of conjoined twin and will likely not result in the other twin being affected by the ingestion of alcohol due to the separation of their circulatory system and GI.

Basically, anyone who shares the same GI and circulatory system should in theory, be affected though the rate and effect of that drug would be different. I don't believe there is any research that studies this in depth so I am only offering my conjecture.