Hi, a separate process is created each time a .cgi script is being requested by the client browser.(If you have mod-perl installed,then I'm not sure)
So, it is possible to have the password file accessed simultaneously. However, if all you do is just reading from the file and verifying your password, then it's safe. If there can be a process which is modifying your passwords at the same time, then you should ensure proper locking of file.

UPDATE: Kindly refrain from ++ my nodes, else Anonymous Monk is going to think that nysus is me or I'm out to cheat xp. : P