Be sure to try the Appliances Forum.

The salesman is an idiot. Period.

You might need that top drawer space for ventilation for the cooktop, as the electronics need more air than a traditional radiant top. Check the clearances specified by the manufacturer. But the ONLY reason that utensils below an induction top would become warm were if there was not enough ventilation. It has nothing to do with the electromagnet field heating them up. A smarter sales weasel wouldn’t tell you such easily disprovable lies. Reading the manufacturer’s installation instructions should be enough education to disprove that. Yet he obviously has not read them.

I agree with Sophie. I don't know which cooktop you are looking at but I know about the Bosch. First, you need a couple of inches clearance at the very back where the power wires come in. That protrudes down about an inch below the rest of the unit, but if your drawer closes then you've passed that problem.

They want 4" of open air space below the countertop, that's for airflow for ventilation, not because it's going to heat up whatever might be in that space. I've measured below ours and while the drawer front sticks up higher, the drawer box itself is well clear (and the stuff in the box is even lower).