32 bit aren't a problem, RAM however could be. I've run Debian on 32 bit Atom netbooks with 1 Gig RAM without problems. Using light desktop environments such as XFCE or smaller ones would allow also 512MB RAM or even less. Years ago I successfully run Debian + LXDE desktop on one of those toy Win-CE Chinese laptops with just 128MB RAM. CPU was a WM8505 clocked at a whopping 300MHz. And then there's ELKS Linux which would work on 8086 CPUs too which I successfully run on a industrial PC many moons ago. https://github.com/jbruchon/elks

Extremely small systems aside, it can run fine on decently equipped laptops or netbooks. Surfing the web with a full featured browser such as Firefox or using heavy apps such as LibreOffice without having the system swap too much would likely require no less than 2 Gigs or more, but if you do network maintenance using command line tools, even the smallest netbook with half a Gig RAM becomes an useful tool to keep in the bag along with bigger laptops.