Well... yes and no.
The attraction was actually going to be called "The Western River Expedition" and was the brainchild of Marc Davis (who came up with most of the pirate gags in PotC). The concept was "Cowboys of the Caribbean"; it was going to utilize essentially the same ride mechanism as PotC, but have a western theme and western gags. The attraction was actually intended as part of a much larger complex called Thunder Mesa, which would have included a runaway mine train-themed roller coaster and trails leading to an observation deck that would give guests a commanding view of the Magic Kingdom. The attraction was budgeted at around $100M -- small change to Disney today, but back then that price tag was exorbitant (the HM's budget was around $7M, by comparison). Thunder Mesa was planned to be added as part of the resort's "Phase II" construction process.
However, three things happened that derailed the plans. First, the Western as a form of popular entertainment dramatically dipped in popularity after the moon landing in 1969 and audiences turned to the skies and science fiction (this turn was referenced somewhat in Toy Story with Woody being replaced by Buzz as a favored toy). Secondly, initial Guests at the resort were outraged that PotC -- which had been heavily hyped by Disney on his national TV show -- was nowhere to be found in Florida. The lack of PotC was, in fact, the number one guest complaint at the MK during the first few months of operation. So, the decision was made -- quickly -- to install PotC at WDW. The only problem: money. So, an abbreviated version of the
Disneyland PotC was hastily installed (which didn't sit well
at all with the Imagineers). Davis was crushed; he knew that the addition of PotC meant WDW management would
never allow the construction of Thunder Mesa. After all, the WRE and PotC was, essentially, the same ride, with a different overlay. The third thing that happened was the energy crisis of '73. Companies were tightening their belts, and WDW followed suit. A large number of Phase II projects were scrapped, including the Venetian, Asian, and Persian resorts -- and Thunder Mesa (now rendered obsolete by PotC).
Elements of Thunder Mesa were paid homage to (or stolen outright, depending on who you talk to) by Imagineer Tony Baxter with Big Thunder Mountain Railroad (the runaway train roller coaster) and Splash Mountain (ride vehicles that would travel out from the attraction into the Rivers of America and then back inside-- and a show scene that was visible from the WDW Railroad. Splash Mountain also used character designs -- and the actual AAs at Disneyland! -- from another Marc Davis-designed attraction, America Sings). Supposedly Baxter was Davis' protege at one point, and the men stopped talking to each other in the 1970s. Supposedly.