Only if it detects it uses a 60W cable. Which I really doubt.

You can pump 100 watts through a 60W rated cable - it will probably work because the rule is "users are dumbasses, rate it for 60 on paper and 120 in reality".

Or it could heat up, maybe to the point of damage.

How do you know?

There is nothing in the cable that would prevent the current from flowing.

The default condition of cables is that they can conduct much more current than is safe, and it takes extra effort to limit this. (Yes, there's a limit to what you can put through a wire, but it's enough to melt the metal, and you wasn't too avoid softening the plastic around it.) If you put twice the rated current through a cable, the conductors will handle it just fine. However, the resistance of the wires will dissipate 4× the power the insulation is designed for (twice the current times twice the voltage drop), and the inside of the isolation will get somewhat warmer. How much of a problem this is in real life depends on the ambient temperature, the thermal conductivity of the insulation, jacket, and wire, the temp the plastics can withstand, etc.

The safe thing is to use wire from a vendor that rates it honestly to conservatively, and start within the ratings.

i live offgrid and observe my 13" MBP with an 85w power supply actually pulling around 10-19 watts during typical usage...(my inverter has an output readout) FWIW... doubtless heavy gaming would be different... compiling gets it up to the upper 30s...