It did for me.
I bought a sealed factory unlocked no sim model MC605C iPhone4 with
4.0.x BB 01.59.,
out of the box.
After unpacking I put in an ATT mini sim I had from my old 4.0.X BB01.59 iphone4 Wk 32 build which got stolen and which I had unlocked to work on Tmo.
Tried to do the tiny umbrella blob save but the Tiny SW recognized the phone but gave a message nothing could be saved.
Then I synced my apps and iTunes in did a backup and then upgraded iTunes 9 to iTunes 10.
Then the ride got a little bumpy.
After the upgrading to iTunes 10 I went for the upgrade to 4.2.1 on the Canadian Fac.
Unlocked phone given I`d read that was doable.
Well after doing that,
I see in iTunes 10 all my previous backups are gone,
the M605C is in restore mode with the screen is stuck with iTunes showing on it.
When I attempted restore in iTunes 10 about 2/3 the way I kept getting the 1013 error.
Read around on the net and came across the "host" fix.
Don`t remember exactly what it is but google windows system32 host etc notepad and you`ll find it.
Anyway after hours of sweating bullets and doing the "host" fix iTunes did restore with no 1013 error and I found the M605C worked was on 4.2.1 BB03.10.01 and still activated unlocked with the mini sim put it.
I`m spent from messing with it so long but I think my old backups are there.
The Apps were.
Navigating the tunes10 is something I`m not up to speed on.
At one point I did get a "Can not sync file not found" error but I read that was solved unchecking sync in Videos/Music/apps and then rechecking em and that worked.
So now I`m good to go till some other quirk raises it`s head but I think
I`m almost at or actually at the finish line.
Your experience may vary.
Write to firstname.lastname@example.org
I`ll help if I can.
Be sure you have an actual Factory (apple factory)
The Canadian unlocked phone activated with no problem.
I swapped out my new cut down Tmo sim and everything worked great.