TLDR: No, they were found all over North America before the Europeans arrived and are being reintroduced into the Appalachian mountains. I can see them preferring the plains instead of mountains in the absence of hunting pressure, but I haven't found any evidence that they were absent from the mountains.
Also, herds of elk are much easier to spot in open plains as compared to forests, that might have something to do with it.
Eastern elk once ranged statewide, but colonization and exploitation by European settlers eventually led to the species demise. Prior to the arrival of European immigrants, elk were found from northern New York to central Georgia. Pennsylvanias largest elk concentrations are believed to have been in the Allegheny Mountains. Elk, or wapitis as they were called by native Americans, were doggedly pursued wherever they could be found in colonial Penns Woods. They were chased with dogs, jack-lighted, tracked whenever snow provided a trail, and shot on sight.
Elk were exterminated in southeastern Pennsylvania and rare west of the Allegheny River and in the Blue Ridge and Cumberland mountains by the opening of the nineteenth century. By the late 1840s, they were gone in the southwestern Pennsylvania and from the Pocono Plateau. By the 1850s, what remained of Pennsylvania's once mighty elk population was limited to sections of northcentral Pennsylvania, predominantly in Cameron, Elk and McKean counties.
History of Pennsylvania Elk
Before the arrival of Euro-American settlers in North
America, elk (Cervus elaphus) were the most widely
distributed species of deer on the continent (Murie 1951;
Gunderson 1976). Its geographic range extended from
southern Canada to northern Mexico and from the Pacific
to Atlantic coast (Wyman 1868; Bailey 1896; Stone
1908; Murie 1951). By the mid-1800s, however, numbers
of elk were declining in the eastern United States. Baird
(1852) stated, “At the present time, in the eastern parts, it
[elk] is only found in a few counties of Pennsylvania . . .
where indeed their numbers are decreasing day by day; a
few are known to exist in . . . western Virginia; it is only
as we proceed farther west that they present themselves
in numbers.” The primary cause of the extirpation of elk
in the eastern United States was market and subsistence
Historic and Recent Distributions of Elk in
North American elk, or wapiti, were once plentifulin the Rocky Mountain National Park area. As Euro-Americans settled the Estes Valley, they hunted elk intensively, sending much of the meat to market in Denver. By 1890 few, if any, elk remained.
History of Elk in Rocky Mountain National Park