Well yes of course it will be recoverable
Or most of it will, even if the drive has been reformatted, which it is likely to have been - from NTFS to Ext4 for instance. The original data is there unless you overwrite it, and a normal disk format does not do that. Adding an OS is likely only to use a small amount of the disk - probably that which used to contain system files rather than data anyway. But it could be rather tedious to restore, and it's likely to have many small holes in it from the formatting process.