I'm back! Been asleep - it's a time difference thing. 
Backtracking:
The range of functions available at the Default Value property in table design is very, very limited - no Nz, no DMax, etc. To examine the available choices click on the elipses (...) to the right of the property and open up the Functions entry by double clicking on it. I don't think you will find your solution at the table design stage.
So you will have to calclate this number at a different stage in the entry of a new employee. You mention:
... self generated number that is created as soon as the Add New Employee form is opened up.
This is not such a good idea: having issued the new number, what if the user abandons the entry? You've stated the number must be contiguous so the only way is to unissue the number - and what if another user has been issued the next number in the interim?
No the best stage to obtain the number is immediately before the new emplyee record is saved for the first time. Use Orange's code but enhance it slightly to test whether the employee number is empty - only retrieve the next number if it is - and to cater for the very first time when there are no records in the table. The event to use is the form's Before Update. So I would expect something like
Code:
Private Sub Form_BeforeUpdate(Cancel As Integer)
If Nz(Me.txtEmployeeNum, "") = "" Then
Me.txtEmployeeNum = Nz(DMax("EmployeeNum", "tblEmployee"), 0) + 1
End If
End Sub
Use your own names of course.
Now what about this multi-user situation. It is possible that another user interferes/overlaps and gets the same employee number. So what to do?
The first thing is to make sure that EmployeeNum (or whatever it's called) has an index and that this index is specified as unique. The first user to use the duplicate number will be successful but the second will recieve a bitch from the JET RDMS and the record will not be added. As I write I do not know the error number but the trick is to trap the error and retry the whole thing again. I'll set up a basic prototype and publish the results for you.