it is possible to use it for deleted files recovery from a notebook SATA hard-drive?
This might depend on the tool, but yes, it should work the same as with a directly connected disk.
Is the data recovery process sending some low level commands to the hard-drive which might be lost if transmitted via USB?
Generally, no. Data recovery software typically just reads data sectors the same way the OS would – it only uses different approaches at finding data that might still be there (e.g. a photo was "deleted", but the actual JPEG data is still there, it's only not attached to a folder anymore).
While it is true that there are many commands that won't work through many USB adapters1, none of those commands are generally used for data recovery. In particular, there is no "undo write" or "recover sector" command in disks – once a sector is overwritten, it is overwritten.2
That being said, some USB adapters don't deal well with damaged disks, e.g. if some sectors are physically almost unreadable, the disk might still keep retrying but the adapter might already decide to "give up". (This may confuse tools like "ddrescue" which try to copy partially damaged disks.) It is often useful to have several adapters that are built with different controller chips.
On the other hand, beware of adapters that translate too much – there exist some which actually remap sectors to a different size (making a 512b disk appear like a 4K one); when connected through such an adapter, the data is technically still there, but at completely different offsets, so the OS wouldn't even recognize completely intact filesystems.
1 This is partly because USB storage devices talk SCSI, not ATA, so the adapter has to translate. (Moreover, "regular" Mass Storage devices speak a very limited subset, while the newer UASP standard is more flexible.)
Many ATA commands have SCSI equivalents and can be translated or at least tunnelled, but a lot of cheap USB-SATA3 adapters don't actually bother to translate all of them – only the most common ones (read, write, identify disk, read ATA SMART data).
As an example, a lot of USB-SATA adapters won't support issuing TRIM commands to SSDs, even though there is a direct SCSI equivalent and a translation could be performed.
2 With lower-density disks, overwritten data could potentially be retrieved using expensive physical inspection (hence the "3-pass DoD wipe" and similar), but nowadays that's pretty unlikely to work.
3 The official name is either "SATA" or "Serial ATA".