Umm,consider this scenario
.An all out conventional war which starts on the pre-text of grave terrorist attacks on India-both sides slug it out for about 15 days & If India plays its cards right-it will have gained territory in Kashmir,Sindh & portions of the Punjab,in adddition to control of Pakistan's SeaLanes.Before such a war goes nuclear Beijing will mobilise it's troops on India's borders to upset India's applecart.Even if China doesn't go to war with INdia,it will not allow Pakistan to sink without a fight.If it means keeping the regime alive in Islamabad by using its diplomatic clout,so be it.Pakistan has been China's insurance policy for nearly 50 years now against India.
In the event of a seminal clash with Pakistan,India will emerge stronger in the long-term,but it would be wounded in the short-term.Trust Beijing to use the likes of Bangladesh or Myanmaar to rub salt.
I think they may well act as you imply, but thye likely ride in as the Islamists "white knight" just a bit too late so that China can maximize its PR advantage of "picking up the pieces".