Matt,
One thing to understand is that Leads and Customers use the same table. The only difference between a Lead and a Customer is a field called IsLeadStatusOnly. When this is set to "True", it signifies that this record is a Lead. All Customers have this field set to False. To see this for yourself, if you export the Customer and Lead table you can see that all of your Leads have this set.
Now going back to your original question, you can absolutely have the grid in the Edit Customer screen. You can still filter by your dropdown since that dropdown would have to be added to the Customer table, which holds both Customers and Leads.
- Adam