Having just had this happen recently, I can only tell you how it worked with my on-board Promise controller on a Gigabyte 7VRXP motherboard. I'll bet it varies by manufacturer and even if we're talking a separate RAID card versus a chip on the motherboard (like I have).
While booting up from power off, the Promise BIOS scanned for drives as usual. Rather than continuing to boot, however, I got a message stating that the one of the drives in array 1 (I only have one array) had failed and the array was "Critical," but that I could still boot (with the single remaining drive). Further, it said to hit CTRL-F to enter the Fast-TRAK (sp?) BIOS and then F3 to identify the failed drive. When I hit F3, it showed both drives without any further comment. One drive is on channel 1, which is IDE 3 on the motherboard and the second on channel 2, which is IDE 4. Neither one was marked as bad. Okay, so that wasn't much help.
What I did then was to open the case and remove the power plug from the second drive and tried to boot up. At this point, the array was not just Critical, but missing all together. Next, I put back the power to the second drive and removed it from the first. I was now back to the array being critical, but bootable. Therefore, I knew that the first drive had failed. I was able to swap it out for another drive and rebuild the first drive from the second. (Be very careful to pick the right source disk when rebuilding!)
As a side note, when I had only the second drive powered up, I hit F3, and it showed the second drive on channel 2 as it had all along, but that the drive on other channel was failed or missing (whereas originally, it just showed the info for both drives). I would guess this meant that the first drive was not totally dead in at least the controller was responding, but that is wasn't able to read and write data. I tried later to reformat the bad drive to see if it would do anything, and it would not even format. I couldn't even read the partition information. It's working enough to return its model number, BIOS rev, and size, but that's about it.