Is it possible to have an effective, working laptop lab with 20-25 computers -- a projector and printer for less than $30,000 -- or less than $20,000?
I'm not sure, but it is unlikely that using free software is going to be the decisive point, particularly if your school does not have any other experience with Linux.
There are only a few laptops on the market that ship with Linux, which basically means if you don't limit yourself to one of that handful of choices, you're paying for a Windows license whether you want it or not. And you're probably also paying a Windows site license of some sort anyhow. I don't understand how that stuff works.
You can save some money using Open Office, of course, if you aren't already. If you've got per-seat licenses on a bunch of other software (Inspiration, etc.) I could point out open source alternatives, but a) you probably don't already spend a lot on this, and b) if you do, you really don't want one lab which has all different, even if ostensibly compatible, software.
Whether or not you can do this depends almost entirely on hardware costs. There are certainly cheap consumer laptops that will fit in the budget, but they'll be prone to breaking, particularly after the three year point, you'll have to refresh the batteries every two years or so, and generally, you'll spend an increasing amount of time castigating everyone for not taking care of the laptops properly, when in fact you're expecting them to hold up to stresses they weren't properly designed for.
More options will be available Real Soon Now, but currently, this is still a not well served niche.