I don't think there is anything in the API to give you precisely that ie for this user check if they have access to this intersection. The closest I can think of is to use the method UserCubeSliceRights. That will return a data table that lists the data access slices and whether the user is in the group. You will have to work out how to process it as the data access slice might be adding or removing access.
Dim ForUser as String = "myuser"
Dim thisDataTableName as string = "SliceAccess"
Using dbConnApp As DbConnInfo = BRApi.Database.CreateApplicationDbConnInfo(si)
Using ds As DataSet = BRApi.Database.ExecuteMethodCommand(dbConnApp, XFCommandMethodTypeId.UserCubeSliceRights, "{" & ForUser & "}{AllCubes}{}", thisDataTableName, Nothing)
If Not ds Is Nothing Then
If ds.Tables.Count > 0 Then
Dim dt As DataTable = ds.Tables(thisDataTableName).Copy
For Each dr As DataRow In dt.Rows()
Dim memberFilter As String = dr("MemberFilter")
Dim userInGroup As String = dr("UserInGroup")
Dim bhvInGroupInFilter As String = dr("BehaviorInGroupInFilter")
' Now process it
Next
End If
End If
End Using
End Using
I have pieced it together from another script but I think it should work.