Any foreign cheques can be encashed in almost all banks. Yes, you need to have an account in any branch.
From my experience.
Federal bank - We get the cheque encashed instantly. Almost same currency excahnge rate.
SBI - We get the cheque encashed instantly. However they give like amount x 35 or so on the same day and rest next day.
SBT - We get the cheque encashed instantly. Almost same currency excahnge rate.
This is applicable for all foreign currency cheques, international money orders etc. In most cases, the banks will take a small fee, like $1 or so.