I know, the title sounds weird :P

After re-stringing my guitar, should I wait before dropping my strings to drop tunings like Drop C?
You can tune it to anything you want. Obviously it won't stay perfectly tuned right away anyway. But if you tune it to C, then decide to go up to standard it may need a bit of time to stretch again.
Well like everyone else said I'd think that you'd just tune it to drop C in the first place. But it makes some sense to tune it to E standard or something first and stretch out the strings Iguess. I wouldn't wait to tune down though if drop C was the tuning I wanted to play in.
Actually, it doesn't make much sense to stretch the strings out more than they need to be if he's always gonna play in C. For drop tunings, less floppy is almost always better.
The only thing I would be concerned about would be making sure your truss rod and all that is in a good spot for a dropped tuning. Other than that tune straight to whatever you use most often.
Fender '72 Telecaster Deluxe Reissue -> Korg Pitchblack Tuner -> Boss PS-5 -> EHX Big Muff -> MXR EVH Phase 90 -> Menatone Pleasure Trem 5000 -> Line 6 Verbzilla -> MXR Carbon Copy -> Boss RC-2 -> Peavey Classic 50
I usually tune to drop D on my 6, and drop A on my 7s. I always tune to standard first then go to drop tuning. (mind you for me that is only my low string) But if I don't do that it seems like it takes twice as long for the tuning to become stable.
Don't go to E first, that's just putting unnecessary strain on your guitar and your strings.
Just tune to what you want and stretch out the strings. A well stretched string wont go out of tune. When I restring I am back to playing about about 15 minutes including the time it takes to stretch them out and check my intonation and truss rod with no tuning stability issues what so ever.
If your playing drop C then Im assuming you'd have some heavy strings. If thats the case definitely dont tune to standard, always leave it dropped at least a half step... I wouldn't tune any differently.. Tune to drop C and play for a while til the strigns stretch