No, a RAID controller should rebuild no matter what once you add a replacement drive. If it's a cheap or onboard controller, the order likely matters. Not sure how Nvidia RAID does it. NVidia NForce RAID may write a header onto the drive, though the first version just kept the drive serial numbers in its flash memory so if the drives were reordered it would adjust for it. Either way, there are only so many stripe sizes supported, so if you keep playing with it and the order of the drives, you will get it eventually with the three good drives.
There are only 24 orders that it can go in, and only half a dozen at most stripe sizes, but that should be pretty easy to determine in advance, just find a block of a known structure and see how far it goes before getting cut off. Look for a piece of the content of ntldr (If it's a Windows NT machine) or something, or just be sure you bill by the hour, though you should be able to work on other projects at the same time.

1 2 3 4, 1 2 4 3, 1 3 2 4, 1 3 4 2, 1 4 2 3, 1 4 3 2, 2 1 3 4, 2 1 4 3, 2 3 1 4, 2 3 4 1,
2 4 1 3, 2 4 3 1, 3 1 2 4, 3 1 4 2, 3 2 1 4, 3 2 4 1, 3 4 1 2, 3 4 2 1, 4 1 2 3, 4 1 3 2,
4 2 1 3, 4 2 3 1, 4 3 1 2, 4 3 2 1