Yes, chances of recovering data from a drive that is completely dead (no power) is very high. Almost always the issue with these cases is either electronics related or bad read/write heads. In either case, it should be a fairly straightforward recovery with very minimal chances of serious media damage.
The only time we’ll see media damage with cases where the drive has completely no power is IF the drive lost power as it was in the process of reading or writing to and from the drive. In these cases, we’ll have to do a thorough inspection of the inside of the drive before attempting any repairs.