You should be able to unclog by 1) removing the cap, 2) let it sit tip-down in a solvent like isopropyl alcohol, 3) press down (without squeezing the barrel) a few times in the process to break the stopper loose, 4) let sit 5-10 minutes, 5) then when you take it out, squeeze the barrel and try to write.
A trace drawn with the conductive ink will combine with solder, provided the soldering temperature does not exceed 350°F (177°C) and the solder joint is formed within 5 seconds. If the drawn trace must be soldered to, we recommended that tin/lead solder containing 2% silver be used and that the trace is heat-cured at 150°F (66°C) for five minutes to produce the most durable trace possible.
For optimal adhesion to most surfaces, clean the repair area prior to ink application. That insures the surface is free of oil, greases and handling soils. For precise cleaning just around the rework area, Techspray offers the TraceTech Flux Remover Pen (#2506-N), which contains a fast evaporating cleaning solvent. Isopropyl alcohol (IPA) presaturated wipes (1610-50PK) are also well suited for surface prep.