There's no way the ad agency or Lucky Strike was going to use the Weavers or any other blacklisted performers. They just wanted to see what kind of arrangement the Weavers came up with. If they liked it, they would have hired four non-blacklisted performers to replicate the Weavers' arrangement.
The Weavers voted 3-1 to do the jingle. Pete participated in the recording session for the jingle and then left the group.