No. Computational, data, and storage costs will be billed against the workspace owner's account.
However, there is a possible workaround if you have multiple collaborators on a project who each have free credits. When the initial workspace owner starts to run low on credits, you can duplicate your current workspace and assign the new copy to a different owner on the team. If you do this, be sure to re-add your collaborators to the copied workspace and make sure to transfer your storage buckets.