I'd be more inclined to say the budget will fall rather than rise. Not because WDI is good with money, far from it. But TDO loves slashing budgets with extreme prejudice whenever they get the chance. I don't know how far this project has gotten to be able to avoid a budget cut, and whether TDO are being kept out of the process. But I would not discount the possibility that the ride's budget will end up below that. New Fantasyland was hit pretty hard with the slashes. And I find it hard to believe they'll allocate more funds just because WDI asks for it. If WDI runs out of cash, we're more likely to just end up with an incomplete ride (ala the descent in Spaceship Earth, the 2009 refurb of Space Mountain and Countdown to Extinction) than upper executives approving more money for it.
Budget cuts are IMHO also doubly possible to happen due to the fact that Disney execs are well aware of how insanely successful and popular Frozen is. They know they don't have to put much effort into the ride to garner interest beyond just linking it to Frozen's name and putting some general Frozen related crap in it. The ride is already being built in a lazy fashion with reusing an existing show building and rumored to be the same track layout as well, I would be surprised if we've imagined the worst of the half-a$$ing it will get before its done.
