Yes, but then the company complains that something it doesn't like is being organized in its property (the workplace) using its resources (employee time, space and electricity for the vote collection/tabulation etc). Plus the people trying to organize the secret ballot are easy to identify.
It's considered perfctly normal for owners of a company to delegate their power and responsibilities to managers, but whenever employees try to delegate things ao tunion 9/10 times the owners scream and cry and allege dark conspiracies.