I think the real question is if the dwarves could get to the mountain in enough strength after fighting through the men and elves. According to the book the dwarves were just attacking between the ford and the spur of the mountain, Bard claimed that they could close in from both sides with their men hidden on the spur of the mountain, but Thranduil wished to wait as long as possible before starting a war over gold. The dwarves guessed they would hesitate and began their attack without warning.
So we have the veteran dwarves, described as "Strong even for dwarves" with mattocks short and short swords, armored head to foot in Iron, set between elves on the mountain armed with bows and spears, and men and elves in the open field.
My guess is that the dwarves are very good against a foe that stands and fights, and there would be very little else they could do the dwarves would break through due to their armour and shields, and occupy the mountain in force.
Tolkien said their plan would be to open another gate, which the elves and men had insufficient men to siege and then they could send raiding parties, and finally perhaps more of Thorins relatives would come, then the elf host and the men would have nothing to do, either stand and die or retreat and forget their gold.
I'd imagine an attack on the mountain would be disastrous, dwarvish fortifications built into the living rock manned by dwarves would be dearly taken.
As, far as Gandalf is concerned I don't know what he could do to stop the fighting, in the book he could because of the goblin threat, but without that how would he convince them?
"The grass withers, the flower fades, but the word of our God stands forever.
- Isaiah 40:8 -