Yes, this is certainly possible. As you may already know it isn't possible to post Instagram posts via Media Injection due to their API, but we do collect the posts and once this is done, you can still assign them to a project.
To do so, go to the 'Project messages' stream and find the message you wish to add to a project and click on the grayed out suitcase symbol. Click the suitcase and select the project you wish to add the post underneath the post.
Please note that it is only possible to add Instagram messages to projects that have Instagram added to their list of linked channels.
Additional information: Note that this isn't just an option for Instagram. Other posts that are published via the channel itself or Facebook ads can be added to a project later on.