Well, I grew up working only with lead free solder (learnt soldering in school in the EU, and RoHS applies for such purposes as well), and honestly, I can't see why they wouldn't. Lead free solder might be a bit easier to work with, but in the end not having a poison everywhere around you is gonna allow you to focus on the real issues instead.

Fume extractors are for the flux fumes, not the (nonexistent) lead fumes. You need them whatever type of solder you use.

There are ways of setting up solder fume extraction that is not intrusive, just like how casinos have HVAC systems that pull smoke upwards and out, generally avoiding the place smelling like smoke. I worked in a service center a long time ago that used such systems and if you shot video at ground level, you would never get any of that equipment in the shot.