That's a lot of backups....
You should be more worried about how you are going to get your RGH to recognize a drive that large. I've never had any luck getting my RGH to recognize an external HDD above 2TB.
You can try adjusting the cluster size of your disk to 64kb, which will then enable the disk to show up in Freestyle Dash, but if you try launching a game from this disk, your 360 will tell you the disk is unreadable and you should try "downloading" it again.
If you want to try and get your drive to work, by altering the partition format and cluster sizes, you can try the following PC Programs:
EASEUS Partition Master Professional Edition
Acronis Disk Director 11
Guiformat
The limits of a MBR (Master Boot Record) partitioned disk top out at 2TB. From there, a disk then needs to be GPT (GUID Partition Table), which your 360 will not recognize. This new type of drive partition (GPT) is recognized by newer computers, if they have a newer BIOS revision (which most new computers have). Sadly, the 360 does not fall into this category, as it is going on 9 years old now.
10 years ago, 2TB drives were not as common (as far as I can remember), so this was not an issue. However, now that large drives are commonplace, this new type of drive partitioning and BIOS revision has become necessary.
If you can get your 3TB drive to work with your 360, and are able to actually play games off of it, please let me what you did in order to do so.
If you are unable to do so, you can always use two 2TB drives, which your 360 WILL recognize.