Yes. Through either imaging or cloning.
Cloning is a direct transfer from the old drive to the new, in real time.
Imaging requires that you make an image file and then restore it to the new drive for it to be bootable.
Both can work. Both can fail. Imaging is more commonly used.
The process can be more complicated depending on the number of partitions involved and the size of the drives and partitions.
The state of your current hard drive might have an affect if it is failing. You might be better off just reinstalling to a new hard drive rather than cloning or imaging. All you can do is try.