The idea that Bitcoin could bail out the dollar in its entirety seems a bit odd given the way dollar debt is created and constantly expands.  The best it seems they could likely do is to recapitalize the dollar based system stepping it up from whatever small percentage of hard assets they have against all of the dollar liabilities to a somewhat higher percentage.  Which would, indeed, at least for awhile, add a degree of robustness to the institutions holding said assets, making them less prone to liquidity risk.

The problem of course is that they'd never get close to 100%, and the liabilities are still expanding, right alongside the ever softening list of assets in the form of various IOU's.  It'd be little more than a slightly reformulated QE.