What would happen if the cell were exposed to a drug that disabled the transport proteins in the cell membrane?

A cell is unable to produce all the molecules it needs to function properly. Similarly, during the metabolism, a number of by-products are released, which are useless for the cell and needs to be removed. Membrane transport of molecules is thus very important for a cell and is needed to allow entry of useful molecules, prevent access to harmful molecules and excrete useless metabolites. Not all the transport can take place on its own and may need transport proteins. These proteins are embedded in the cell membrane and are responsible for cross-membrane transport of a large number of useful molecules, at the expense of energy. Thus, they participate in the active transport of molecules and are necessary for cell survival. 

If a drug inhibits the activity of transport proteins, active transport of large molecules, such as glucose, ions and amino acids, will stop. An absence of these molecules will simply kill the cell. Functioning without transport proteins is similar to trying to breathe with your nose and mouth clamped shut. 

Hope this helps.