I host movie nights with friends and sometimes someone might even smoke in the room, air purifier clears the air quite fast and there absolutely are no odors left. So yeah you can and if you solder or 3d print often, I'd suggest to get one, they don't cost much.
I'm not allergic and air here is basically always perfect - 1-5 ppm, but I still love it. It does filter out allergens and people allergic to pets find it easier to breathe (I have a dog). It also lowers amount of dust a bit, and I have an automation to run it on full speed when robot vacuums floors, I think it might help filter some stuff out.
I wish there'd be a way to put activated carbon packs inside somehow, because I'd love to change it more often than the full filter.
https://www.vevor.com/fume-extractors-c_13369/vevor-38w-desk...
if you do use a filter make sure it captures metal vapor, which is unlikely with a regular hepa filter.
Laser cutting or engraving makes even worse fumes and requires seriously good filtering. I personally think they're nasty enough that it is irresponsible to just dump this stuff outside into the environment without cleanup but it's certainly better than breathing it.
Seeing as a lot of solder is lead based i imagine this would be a huge safety concern if it did create lead vapor.