Do you mean the leaflet website, or the leaflet maps library itself?

I see the http://leafletjs.com website uses some google fonts, and google analytics, but I would have thought it would degrade gracefully if those things are blocked.

As for the leaflet maps library itself, this will definitely operate independently of google or twitter. Try here for a simple example embedded on my website (with no googleness) http://harrywood.co.uk/maps/examples/leaflet/1-just-map.view... or even better, try here where I'm loading it from locally hosted javascript: http://harrywood.co.uk/maps/examples/leaflet/1b-local-osm.vi...

Those links working for you?