For projects of this size I'm betting they do. For one thing, the SFWMD permitting process involves calculations of things like rain runoff from roofed buildings.
Blueprints are also used to get bids prior to going to the board for budget approval. I think for something the size of Villains, the board has to approve twice (once for the internal budget estimate, and once again when bids are in).
I was told earlier this year when asking around about a 5th park that the board gets involved with anything over $1B. (And the board had not heard anything about a 5th gate at that point.)
Epic Universe had work started before it had blueprints ready. You can start building a site to host buildings without knowing what those buildings are or will contain. Most new build attractions start construction before design work is complete.
The water management permit has already been issued. Most projects use more specific calculations because those numbers are readily available as part of the design process, even early in the process. It’s also not that difficult to get modifications (see Ratatouille and the addition of the crêperie) But you can also apply for permission based on general areas because the calculations are really about impervious areas and a roof is not functionally different than a walkway.
Large projects like attractions and lands do not use the design-bid-build project delivery method. Disney instead utilizes IDP (integrated project delivery) with aspects of fast-track project delivery. IDP involves hiring the general contractor during the design phase to assist with coordination, estimating and provide input on the constructibility of the design. The online posting for contractors even listed the project as being “design-build”. Contractually, design-building usually refers to hiring one legal entity that is legally permitted to handle design and construction, but it’s a similar enough idea to IDP of hiring your design team and construction team together and having them work together. Fast-track is the overlapping of construction with design, starting construction before design work is complete. Disney is also a bully when it comes to purchasing and pricing, and they will often buy a lot of the base construction materials that are typically purchased by the contractor.
Estimates are put together multiple times throughout the design process starting as early as Blue Sky. At a minimum, reviews would occur after every phase of design, but can also occur at different points. The major “Go - No Go” decision occurs after Concept Design and is the Feasibility phase. This point is also a major contractual point as design vendors are hired through concept but then separate contracts are proffered for the rest of the project (schematic design through construction). I can’t speak to subsequent reviews/decision making by the board for high cost projects, but they definitely feel like something that would be clouded by the sunk-cost fallacy as there would already be some work completed on site. They could though be involved in deciding if a project should receive additional funds or if the team needs to figure out how to keep things on budget (usually scope cuts).
All of the phases of design have drawings that would be called “blueprints” but they’re not yet part of the complete package of information required for construction. The construction drawings that are not even the only documentation provided, as there is also a massive project manual that outlines the work and performance requirements expected of the contractor.