Hi Boom,
It is possible, but first confirm it is the hard drive and not the caddy. Try the HDD in the PC or using another caddy first.
Altough, the buzzing sound does sound like HDD failure to me, they are extreemly sensative to this kind of damage. Repair is possible, depending on the extent of the damage, but can be very very costly. There are companies (such as
Data Recovery & Hard Disk Information Retrieval - DataClinic UK) that specialise in HDD repair and data retrieval. It all depends on how important the data is to you. Treat this as a learning experience also, make sure you backup any data that is important to you, as HDD do also have a limited life span.