You could, assuming you can install another internal drive, copy the data from the drive to the replacement. I would suggest cloning that drive using a program such as Macrium Reflect Free but if the drive is failing it may not clone properly (may be unable to read the entire drive). If that is not practical you could use a drive enclosure or docking station and connect the new drive externally. 
I noticed that my XPS 8930 is hanging whenever I access application data stored on the drive (2TB SATA) I ran ePSA Pre-boot which resulted in Alert 2000-0151, validation 113331. CHKDSK reports drive is ok. My system is out of warranty. I ordered a replacement drive from Dell. My data is fine -I have not lost anything. The PC boots just fine. I would like to just copy all the data from the existing drive to the new drive. Would appreciate any suggestions as to how to do this seamlessly. The SSD C: is fine.     
XPS 8930, secondary hard drive (D) failing