If an external HDD's USB port gets busted, will plugging the HDD's SATA directly to a PC possibly work?

If an external HDD's USB port gets busted, will plugging the HDD's SATA
directly to a PC possibly work?

My Western Digital MyBook Essential crashed recently, and I'm unable to
access it through Ubuntu nor Windows.
My goal is to recover my data, and wondering if it's advisable to connect
the HDD directly to the PC thru SATA, and then recover the data using a
recovery tool such as Recuva or StellarPhoenix.