No. The Annual Pass is only valid at participating Federal Recreation Sites.
State Parks & National Parks are owned and operated by different entities so their passes cover their specific parks. Our America The Beautiful Pass covers entrance fees for approximately 2,000 different National Parks, Monuments & Federal Recreation Sites and is valid for one year from the date of purchase. Most States offer their own seasonal/annual passes for the parks they own & operate.
Depending on the parks and sites you plan on visiting you may need a State Park Pass & a National Parks (America the Beautiful) Pass, checking the websites for the individual parks will provide you with necessary information as it should list the park passes they sell/honor.