No. The Appalachians are an eastern mountain system. They stretch ~1,500 miles from Newfoundland, Canada, to central Alabama, USA—paralleling the Atlantic coast.
The Rocky Mountains are the great western range, running from British Columbia to New Mexico. The two systems are separated by the vast Interior Plains (Prairies/Great Plains).
Confusion sometimes arises because the Appalachians' westernmost ridges (e.g., the Allegheny Front) reach into eastern Ohio and Kentucky, but they never approach the continental interior or the West Coast.