That is not how this works. This is not how any of this works.
First of all, there is no power going through any active or passive components on the motherboard. That's just plain traces, so unless the board is significantly undersized and catches fire, almost nothing to worry about.
Second, current follows the path of least resistance. If the card draws a majority of the power from the motherboard, it's because the resistance is marginally lower on that path, and AMD isn't actively balancing the power draw.
With more cards added, and even the slightest voltage drop on the motherboard - and be it only a few dozen millivolts, the draw will invert. Heck, in extreme situations, such as an Etherium mining rig, you probably won't even see more than 20-30W per card being drawn from the slot, and the rest being drawn from the 6-pin connector (which itself can easily take that power draw!).
What you *should* be worried about is spikes in power draw due to insufficient capacitor capacity on the inside, disrupting the system stability. But I don't see that happen, given that the VR setup of the 480 is pleasantly oversized.
Just to add.
The context though is the specification of the 24-pin ATX socket in terms of power (2x12V pins) supporting all slots and other power, the riser socket, and the 6 (2x12V pins) or 8 (3x12V pins) Molex connectors, PSU rails for the 24pin connection and also PEGs, wire gauge (can be specc'd 16-24 AWG).
The 24-pin with regards to the ATX12V guide can be specc'd depending how implemented roughly from 8 to 13 amps for each of the 2x12V pin, and peaks roughly of 9 or 16 amps respectively although this is burst with around a 10-20ms duration limit I think.
The Molex PEG pins also support 8A minimum and up to 13A per pin depending again upon spec implementation.
The riser slot I have no idea but this is not guaranteed to be much more than 7-8A, and some extension risers are even less.
Cable is commonly 18AWG for the auxiliary PEGs, which is good enough to run 8.5A per pin (contact), the higher specification of 13A will require 16AWG.
For the 24-pin ATX12V, best to check the motherboard and cable to see if it is 16AWG and whether the motherboard defines connector as standard/HCS/Plus-HCS - unfortunately can be difficult information to get.
So the 480 does have some considerations if going 2x480 or overclocking as it is pushing hard against the limits or beyond, along with consideration of how low-budget PSU and motherboards can handle the sort of characteristics picked up Tom's Hardware - caveat being further investigations are required to prove this beyond theirs and some other reviewers' tests to date.
But this is all from the context of power demand and distribution that has arisen from some reviews.
Cheers
Edit:
Regarding the ATX 24-pin there is also a definition for 450W-ATX12V, supporting 16A max with peak (I think 10-20ms burst) of 19A per connector.
Thought I better mention it, even though its context is far away when one considers the mainstream consumer 480 GPU.