No, you cannot submit campaign-required work on the community homepage. All of your work must be submitted under the "Submit Work" tab of your Campaign page.
Please note, if you are using the Co-Promote page with your Community:
1. You will still need to submit your own work using the "Submit Work" tab on the Campaign page.
2. You can submit your Social Community Shares (re-syndicating, re-posting, sharing community members' work) using the Co-Promote page. You will use the social media buttons below each pin. You will not need to submit these links anywhere else.
Read this blog post for more information.