No they don't.
All they can "see" is the surface temperature of the tarp itself, which can of course be affected by what's behind it.
But depending on the ambient temperature around the boat, you might not be able to see any indication at all someone is inside.
The boat in Watertown was covered with shrink wrap white plastic, not a normal poly tarp. Based on the FLIR images released from the police helicopter it looks like the plastic film was pretty much transparent at the IR wavelengths being sensed by the FLIR device. Image quality of structures within the boat looks much better than would be possible from re-radiated energy from an opaque surface.
You are correct of course for a cover which is opaque at the sensing wavelength.