Answer:
No.
Explanation:
Let's assume that the average drop is 0.05cm³.
0.05cm³ * 78000drops/sec * 60secs * 60mins * 24hrs = 336,960,000cm³ which is more than the volume of the room.
In order for the locksmith to arrive in time the average drop would have to be less than 0.00056cm³ which probably isn't happening here. And even then the gerbil has probably already drowned unless its cage is at the very top of the room and the locksmith is a wizard.