Highly unlikely. If your Pulumi project is logged into one backend to do its work, then needs to log into another backend to get some data, then it would (using current architecture) need to log out of the current backend.. which would stop the current work.
If you need this to work, you need to work around it. For example, instead of using Pulumi stack references to get values from one backend to another project, you could have the first project push the important data to well-known vaults, SSM parameters, or anything like that. Then all other projects could get the values from the well-known shared locations, rather than from Pulumi state.