Precision just makes the missile land in the right square.
Blowpipes work the same way as poison arrows, as everyone said. Except there is a MR roll to resist the blowgun poison (Which is actually 50-damage stun damage, not paralyzing poison as the description says. The effect is immediate and does not divide stun across turns the way poison divides damage across turns).
From the debug:
blastsqr: unr17793 x43 y23 aoe0 dmg0 eff109 spc1075838977 as-1 al0^M
blastsqr: unr17793 x43 y23 aoe0 dmg50 eff46 spc1073754240 as-1 al0^M
affectvic vic15643 hv0^M
hitunit 17793 15643 dmg50 spec1073754240 ba4^M
spec_mr pen 12 mr 18 (unr 17793 vic 15643 dmg 46 eff 50)^M
resisted^M
That's a square with unit #15643 getting hit with a dart. It does no damage, and the unit passes the MR check. Later:
blastsqr: unr17798 x43 y23 aoe0 dmg0 eff109 spc1075838977 as-1 al0^M
blastsqr: unr17798 x43 y23 aoe0 dmg50 eff46 spc1073754240 as-1 al0^M
affectvic vic15643 hv0^M
hitunit 17798 15643 dmg50 spec1073754240 ba2^M
spec_mr pen 12 mr 18 (unr 17798 vic 15643 dmg 46 eff 50)^M
Oh, that's bad! No "resisted", so fatigue is increased, from 22 to 40. That stun damage (28) looks about right for a 50-dam attack on 22 protection.
Anyway, nice use of the Blowpipes! I've never managed to get them to do anything useful.