Possibly, depends on a lot of factors. Positive/Negative pressure and overall airflow.
If the overall system is under negative pressure, that would mean cool air coming in through the exposed holes (along with dust). Under positive pressure, that would mean additional exhaust despite there being no fan there.
The entire idea behind cooling is getting the components to spread the heat around to the environment. Closing off anything means you are changing that dynamic a little bit.
If the exhaust fan is the only way out of the case due to the tape, that means the only intake is coming from where?