No, it would be a problem. Gravitational collapse would heat up the sun's core via the Kelvin—Helmholtz mechanism, which was proposed in the 19th century as a mechanism for the burning of the sun. If that were happening, then some of the energy emanating from the sun would be from gravitational collapse; ie, only some of the energy would be from thermonuclear fusion.
Our mass-loss figure is calculated with E=mc2. First we measure the total energy output of the sun per second, and then we plug that value in for E and solve for m. If less than the total energy output is due to fusion, then less mass is being lost.
I'm pretty sure this is false according to relativity, and that the energy released by gravitational collapse does contribute mass when in it's potential form, and so mass would still be lost in equal amount if the same quantity of energy is emitted via gravity collapse or nuclear fusion.
But this is only by intuition, I may be wrong so input by Cavediver or anyone else would be appreciated.
Edited by slevesque, : No reason given.