Can anyone submit a letter of determination to the IRS asking them to determine if Uber is operating legally with regards to its independent contractor worker classification?
I doubt it. But anybody can tell the IRS that they believe a person or company isn't paying their full share of taxes. I suspect that the IRS would prioritize complaints from, say, disgruntle corporate accountants, but it should be possible for anybody to report what they believe is tax fraud.
The IRS probably already knows about Uber. They probably haven't audited the company or asked for details, but they must be vaguely aware of how the company operates.
