Theoretically third-party candidates could gain exposure through the General Election debate however, the Commission on Presidential Debates which organize the debate makes it very difficult for a third-party candidate to be eligible to the debate. Indeed candidates need "a level of support of at least 15 percent of the national electorate as determined by five selected national public opinion polling organizations" as defined by the CPD.
You may then wonder who is the CPD? The CPD is a PRIVATE organization financed with PRIVATE money. They claim to be nonpartisan even though it is governed by former chairmen of the Democratic National Committee and Republican National Committee. No wonder why they don't want to open the door to third-party candidates...