How can a pre-main sequence star radiate more energy by gravitational contraction than a main-sequence star can by hydrogen fusion?
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Although pre-main sequence stars have lower temperature, they are essentially huge clouds of gas, often as large as 1 pc wide. The luminousity being proportional to square of the radius is essentially large for pre-main sequence stars.
Plus, the problem with gravitational contraction is not the amount of energy that can be generated per second. That can actually be larger than that produced from fusion if you insist on really massive objects. The logic, when we ruled out gravitational contraction as a source of energy for Sun, was that gravitational contraction cannot sustain it for long. Geologists knew from their dating science that Sun had to be older than grav. contraction accounts for.
Thus, admit it. Gravitational contraction makes pre-main sequence stars radiate more energy than main sequence starts, but that's just luminousity and not really energy. Luminousity is energy per second.
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The luminosity of a PMS star is provided by the rate of change of gravitational potential energy as it contracts.
Since PMS stars contract along Hayashi tracks at almost constant effective temperature, their luminosities decrease considerably with time as their surface area diminishes. However, the virial theorem tells us, that the core temperature of the PMS star must increase, roughly as the reciprocal of the radius. Ultimately, this leads to the ignition of hydrogen, but the rate of nuclear burning only ramps up to be equivalent to the luminosity at that point. Therefore the luminosity of a main sequence star is generally$^1$ lower than during the majority of the PMS phase for a star of the same mass.
$^1$ This is not always true. There can be a brief phase of constant or slightly increasing luminosity just prior to hydrogen ignition that is caused by the development of a radiative core - called the Henyey track.
