Yes, government employees can open their Demat account with any broker in the stock market. There are no restrictions by SEBI for government employees. However as per the guidelines given by Central Service Rules,1964 -
No government employees are allowed to speculate in any stock, share or other investment.
No government servant shall make or permit any member of their family or any person acting on their behalf to carry out any investment which is likely to embarrass or influence them in the discharge of their official duties.
To understand in detail, refer to Central Civil Services (Conduct) Rules, 1964, (page 12 for Investment, lending and borrowing by govt employees).