Yes, SURGERY is a Scrabble word!

Letter values in Scrabble US: S 1, U 1, R 1, G 2, E 1, R 1, Y 4.

Is it a valid word?

SURGERY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

the branch of medical science that treats disease or injury by operative procedures
a room where a doctor or dentist can be consulted
a room in a hospital equipped for the performance of surgical operations
a medical procedure involving an incision with instruments; performed to repair damage or arrest disease in a living body

Also: operating room, operating theater, operating theatre, surgical operation, surgical procedure, surgical process.