YES, You Can.

I don't know about other Banks. But Go to Doha Bank.
You can open only Current A/C
Documents Required
1) Valid Passport Copy
2) VISIT VISA Copy (Visit VISA sponsor should be Employer/Company)
2) Appointment Order from the Qatar Employer
3) Request letter from the Employer Stating you QID is in Process
4) One month Salary Slip.