The indicator circuit is wired so if it blows the tubes will still run anyway.
That is true in every circuit that I am aware of.  If the 1N4003, 330 Ohm, or the LED itself fail then then whole indicator circuit is non-functional no matter where you connect it.  
The amp itself is what you still want to work in the end, all else failed. If the relay supply fails you only lose the relays with no interruption to the amps function itself, keeping the low voltage/high current winding in the main PT dedicated to powering the tubes and that's it. 
Yes, the amp will still work if the 7812 fails and the PT does not.  Ideally, I want the power indicator to tell me if the amp actually has power to the full circuit.  In this case, the amp should only work properly when the power indicator indicates power.  It is always possible for any amp to work with no power indication if the indicator circuit fails.  This is obvious.  But, this can also happen if the indicator is connected to the 7812 output and the 7812 fails, also a bad scenario.  If you wire the indicator to the 7812 output then you have the following situations:
1 - The indicator lights.  This indicates that the relay transformer and 7812 are working, but tells you nothing about PT operation.  This is just a relay power indicator and not a 'real' power indicator.
2 - The indicator does not light.  This indicates one or more of the relay transformer, the fuse, the power switch, the indicator circuit or the 7812 have failed.  In some of these cases, the amp will still work even with no indication.  This is not good behavior for a power indicator IMO.