No, Epcot's attendance didn't drop until it got stale in the early 90s. Contrary to the urban myth that EPCOT Center was initially a failure, it was extremely popular. Heck, it was even featured on VH1's "I Love the Eighties"—it was really that much of a cultural icon!*
I think most of the "EPCOT Center was a failure" myth comes from how Guests asked where the Disney characters were. People didn't leave because of that; they just wanted to know. Disney added them, and EPCOT did just fine. Some vocal critics also complained the EPCOT was too commercial, but they completely missed the point—it WAS a permanent World's Fair.
Anyway, Epcot got stale in the early 90s, and by the mid 90s, it was basically just a set of omnimovers while the MK had Splash Mt. and AE, and DMGM had ToT.
*And you can watch Justin Timberlake say it was boring, while everybody else says they loved it. Nobody ever said Justin was smart.