No way.
What one needs to understand is that most headphone amps can only put out a very low amount of current (which effectively translates to limited power) and speakers are much lower impedance devices than Senn HD's (they suck up a lot more power.)
To get some idea of the difference.....
If you are driving Senn HD580's to peaks in the 100 to 105 dB range, they require a signal of about 2.0 volts.
power = voltage squared/impedance
4/300 =
0.0133 watts (13 milliwatts)
Speaker sensitivities tend to be around 90 db at 1 meter at 1 watt for a lot of 8 ohm models--which is exactly what Polk specifies for the RTi8. The Crown Audio web site has a calculator for sizing power amps for sound reinforcement, but the calculation holds for any speaker/amp situation:
Amplifier Power Required Calculator
Let's assume that the listener is 3 meters (~10 ft) away from a speaker that has a 90 dB per 1W at 1 meter sensitivity, and that the listener still wants to listen at a level requiring 100 dB peaks......plugging those values into the calculator, we find it requires
90 watts power to drive that speaker (setting the amplifier headroom in the calculator to 0 dB to find the actual power required, not with a safety factor to prevent clipping.)
So, the speaker will require 90/0.0133 or
6,766 times as much power to achieve the same volume as the headphones.
The other issue is voltage. If an 8 ohm speaker requires 90 watts to reach the peaks, the power amp output stage must be able to supply a 27 volt signal.
The power supply for the 0404 USB is basically a 5 volt, 1 watt supply.
I hope that makes it clear that why a typical headphone amplifier cannot drive speakers.