Other places where you can see this concept is the Orions Arm hard SF universe or the old Imperium Galactica RTS. :)
I'm unconvinced. We are firmly in the realm of thought experiments, of course, but I think all this would do is produce changes within local maxima, the reason being that even while adapting to new living conditions, evolution only has so much to "work with" from within the local maximum given by the existing human body.
In contrast, a mass extinction event looks closer to pushing a big reset button, radically shaking up existing lifeforms and giving other struggling species their chance at the limelight. Maybe even species that right now are microbes or invertebrates, but that -- should mankind, mammals and birds go extinct -- would evolve into dominant lifeforms, filling the vacated niches in the ecosystem.
Maybe the species which by our continuing existence we are potentially preventing from becoming dominant is the species that would have successfully colonized the solar system and beyond, instead of us. Not a variation of humans under new conditions, but a radically new species unrelated to us.
It could even result in funny situations where one of them encounters a clearly alien beings with totally different physiology, culture, appearance and language - only ot find they are just another branch of life originating from Earth. :-)