No. Reports are not designed to be “interactive” in that manner. I can understand you want to not need to create Entity Screens, but you still have options.
The Report Widget in an Entity Screen can be set dynamically to display whatever report you want. So you can still have 1 Entity Screen, with a search function, and based on the return of that dialog, you switch the Report that is in the Widget, even supplying parameters to the Report.
For example, way back when, I used to flip reports in/out for the Payroll (several Reports, 1 per employee that were all the same, except for the Entity that was hard-coded in the Report). That was done with Set Widget Value action. So that should work for you.
Now I don’t bother with having a separate Report per Employee; I have 1 Report that has parameters, and I just refresh the Report by sending in different parameters with Refresh Custom Report Widget. In fact, that should work for you too. That Action, IIRC, has a parameter for the Report Name as well as parameters.
You could basically build your own mini Report Explorer if you want, but with much more functionality. In fact, I never use the Report Explorer because of it’s lack of features, like parameter support.