"The disk might contain viruses in it."
-Yes, theoretically. You could scan this drive with your AV before doing adding data or doing any other tasks on the new drive.
DBAN is more about keeping others from accessing your old data when you sell an HDD\SSD (bits of which can be left after reformatting).
If you do a full (vs quick) reformat of the drive it should wipe out any potential Virus.
However, some virus inhabit the boot sector (if the drive was used for Windows previously). In this instance deleting the
virus may be a bit more tricky.
I don't recall the methods, but you should be able to find a few tutorials with a www search.
.