[How] can I be sure that this PDF generated from InDesign will print to paper as it is shown on screen in PDF ?
There at least a dozen variables in the path from screen to press. You can not control all of them and it's entirely possible ones you can control are incorrect.
You have to calibrate everything - monitors, scanners - use proper profiles for all application and images - export to a press-ready (PDF) format and then get a chroma key/color proof from the printer.
Once you do this a few times you'll begin to trust your settings. However, there's never an absolute way to know that everything is perfectly correct until you see the file off the press compared to your screen.
I am not a Corel user. But I am a long time InDesign user. If you've got your monitor properly calibrated, your InDesign color settings correct, and exported to PDF/X format, chances are you're pretty close with the PDF generated from InDesign. However, only a chroma key or press proof will verify that.