Does a bare arctube from a HPS lamp emit UV?

Yes and even shorter wavelengths then MV (those the quartz does block)... Not a good idea to operate it in that way...

But bare HPS arctube does not warm-up to normal temperature without the hard-vacuum thermal insulation, so the sodium pressure is too low to suppress the Hg and Xe radiation, this effect being worse for lower wattage lamps.
Furthermore the 2W of UV output is way too much for "safe lamp" and due to the effect above, this figure would not reduce at all for lower wattage lamps (it might even be worse).