No. The Time and Expense user's security profile does not grant permission to access the Projects screen. Check CORE Help Center for details.
If you customize the security profile of the user to grant them access to the Projects screen, they will still not be able to see anything unless they also have the proper subscription package assigned to them that will allow them to access the project management features in BQE CORE. Please check with your Sales Account Manager to purchase the required subscriptions.