Matt, if the RAID status appears as Failed, most likely it could not be recovered.
If the system is booting to the operating system using the other 2 hard drives, then the array is OK.
But in the other hand if the array appears as Failed in the RAID BIOS, means that the RAID structure/array has a problem and unfortunately there is no way to know if the rebuilt is going to work as expected. What we recommend in these cases is back up all the data.
Once you backed up all data, you can connect the new HDD and let the rebuild begins.
Usually, the storage controller initiates the rebuilt by itself. If it does not start, it will be necessary to go to Windows and choose rebuilt from the Intel® Rapid Storage Technology.
Would you please access the RAID BIOS in Ctrl+I and send me a picture of the screen?