Yes, but not recommended. USB hard drives draw more power and rarely improve speed because the 360’s USB is the bottleneck.
: Use USB 2.0 or 3.0 drives (though the 360 only supports 2.0 speeds, 3.0 drives often have better flash memory). SanDisk Ultra USB 3.0 : Reliable and widely available at retailers like Samsung BAR Plus install games xbox 360 usb best
If using a thumb drive, ensure it has at least 1 GB of capacity. Be aware that many flash drives may fail the console's initial speed test or experience performance issues if they are rated below recommended speeds. How to Install Games to USB Yes, but not recommended
Use USB 3.0 drive (backward compatible) with 64 KB cluster size when formatting FAT32 – reduces stutter in open-world games. SanDisk Ultra USB 3
Re-format it on a PC using FAT32, then re-format on the Xbox. Some drives have controller sleep issues. Avoid "green" eco-friendly drives.
To install and play games on an Xbox 360 using a USB drive, you must first format the drive to match the console’s specific requirements. While older updates limited USB storage to 32 GB, modern firmware supports up to of external storage. 1. Best USB Drive Requirements