Will this trigger always complete before returning results of Insert to client?
DELTE the UPDATE from your trigger

CREATE OR ALTER TRIGGER dbo.TR_MyTrigger ON dbo.Cust
    AFTER INSERT, DELETE
AS
BEGIN


When you delete the UPDATE trigger Case 4 and 3 wouldn't fire the  trigger again.

So only when you INSERT or DELETE, the trigger would run, and update Cust or insert into AuditEntries 

With this AFTER UPDATE TRiGGER you would create a loop.

so you should write another triigger only for UPDATES, if you need one.

To answer your question

The trigger would run after the INSER or DELETE of dbo.Cust and will  run completely before starting another command, that is because you define  your trigger  as FOR EACH STATEMENT 

As Example 


INSERT INTO dbo.Cust VALUE (1,),(2,),(3,),(4,),(5,)
TRIGGER dbo.TR_MyTrigger
INSERT INTO dbo.Cust VALUE (6,),(7,),(8,),(9,),(10,)
TRIGGER dbo.TR_MyTrigger
DELETE dbo.Cust ...
TRIGGER dbo.TR_MyTrigger#


Every step is completed before the next