Yes, but it's actual effort not perceived effort that matters. It takes a certain amount of energy to move a rider and bike from point A to point B at a certain speed, no matter how hard the rider perceives the effort to be. It doesn't matter if one rider can do it at 60% and another needs to haul at 80%. The energy requirement is the same. The energy requirement is completely independent of the source.

Where HR factors in is when you go over AT and the burn rate jumps. But the Edge doesn't know what the AT is, anyway. Apart from that air resistance, rolling resistance, weight -- all the usual factors -- apply. But HR isn't such a big factor. You also don't really care about the fat burnt (at least I don't), only the repletable glycogen, perhaps the Polar unit tries to estimate this and doesn't even report the fat part since it doesn't really matter.