It might seem apocryphical, but I do remember back in the mid 1990's DC did a Green Lantern Annual that broached just this subject!
Granted this was Hal in his Parallax identity, searching out Alan Scott's power Battery with Kyle as Green Lantern becoming embroiled with stopping his efforts. Hal tries tapping the mystical Battery's power and some side-effect sends Kyle and he through time, where Kyle finds himself back in Hal's earliest days being 'Hal', as Green Lantern.
At the end of the Annual (possibly part of the Year One brand) Hal abandons his efforts with Scott's Battery, the power too uncontrollable and unpredictable.
I think if you bear in mind the reasons the Guardians collected mystical energy from their Main Battery and inadvertently created the Starheart the proof does show that that power is indeed volatile and only able to be wielded by very particular and selected people. Alan Scott was chosen by it, for whatever reason he was selected as fit to use it, and I am not at all sure that despite his willpower and experience in standard Power Rings and the Emotional Spectrum Hal could gain the control of the Mystical Green Flame... as by its nature this power and Ring is very different to what he is accustomed to wielding, I would even suggest it isn't at all compatible to his will and rigid outlook.
Of course, on the other hand there was that story in Green Lantern Quarterly where a visiting Abin Sur briefly used Alan's Ring to foil some intergalactic crooks he had pursued to earth... but with the revisions to the mythos and the positioning of the Green Spectrum at the center of the Colour Spectrum it does make sense that the wilder energies of Alan's Ring would be as difficult for Hal to wield as the Blue, Yellow, and Red Spectrum's were - Green Will is what he specialises in exploiting, and that is due to it being the most stable of the Emotional Spectrum range. Everything else he has struggled to use, yet alone master as he has the Green light.
I believe they have shown that just by staying green they can increase his power and abilities just fine.
If they continue to go down this path (they have chosen for Hal), he will continue to become more powerful as I do believe he is still changing and learning what exactly he can do. Removing his self imposed limits, and reaching his full potential.