Definitely. Those fumes are just flux smoke, though, but they are still to be avoided. In my prior life I used to deposit thin films of various metals including lead to make superconducting tunnel junctions. I have a vapor pressure table for lead somewhere in my library, but as I recall at the low temperatures you use for soldering lead alloys there is no danger (tin-lead eutectics melt at a much lower T than either tin or lead, and I had to use higher than melting point temperatures for depositing films).
If you want even more boring stories about lead, I can tell you about the hazards of lead plating out from radon gas, or our use of ancient lead from Phoenician shipwrecks as shielding on a dark matter search experiment.