Ok so the subject looks like a stupid question but bear with me 
As per my previous post, I've been migrating our DCs to new 2012 R2 ones. This has all gone fine.
Of our two old 2003 DCs, I've demoted one of them back to a member server. In order to test everything is working correctly this week, I've now turned off the last remaining 2003 DC. I intend to leave it off for a week or so to check for any remaining issues (odd machines still pointing at it for domain services etc).
My question is, once this period is over and I'm happy, should I just leave the old server switched off (and eventually scrap it) or should I restart it, let it sync back up again and then demote it properly?
I don't care about the old machine as it'll be scrapped either way, I'm more concerned about whether I should properly demote it to remove all trace of it from the domain or whether I can just leave it disconnected and possibly perform a little manual clean-up of AD?

As per my previous post, I've been migrating our DCs to new 2012 R2 ones. This has all gone fine.
Of our two old 2003 DCs, I've demoted one of them back to a member server. In order to test everything is working correctly this week, I've now turned off the last remaining 2003 DC. I intend to leave it off for a week or so to check for any remaining issues (odd machines still pointing at it for domain services etc).
My question is, once this period is over and I'm happy, should I just leave the old server switched off (and eventually scrap it) or should I restart it, let it sync back up again and then demote it properly?
I don't care about the old machine as it'll be scrapped either way, I'm more concerned about whether I should properly demote it to remove all trace of it from the domain or whether I can just leave it disconnected and possibly perform a little manual clean-up of AD?