No. Not screwed.
If the tables have a relationship through EmployeeID, you actually prefer the names to be the same. If two tables holding EmployeeID have a common relationship with a third table also holding EmployeeID, this also is acceptable.
If the tables aren't related, there is no TECHNICAL reason you couldn't do this, though I would worry about the confusion potential. Nonetheless, all you have to do in this case is to qualify the field name with the table name.
Like, [Employees].[EmployeeID] = [AssignedProjects].[EmployeeID]
See, no sweat! Just a little extra typing, that's all.