“building=collapsed” will this tag be visible on the map ?

The standard 'Mapnik' render is not designed as a crisis mapping platform. Just as it is also not the best map for planning cycle tours, MTB biking, white-water excursions or a host of other activities which have specialist dedicated maps produced from OSM data. Please remember OpenStreetMap is primarily about creating geographical data: rendered maps are just one of the ways which this data is consumed.

Suitable visualisations of crisis related data are available: for instance those made by Pascal Neis, or the POI map or the damage overlay capabilities of All-in-One map for Garmin devices.

If you have a look at the wiki, it reads

It is common to use building=< building typology > if you have this information. Renderers are free to support these or just treat them as synonyms for building=yes.

As you can see Mapnik seems to treat 'collapsed' as 'yes'

This depends entirely on the renderer used.

The tag was strongly used after the Haiti quake, see e.g.: http://tagwatch.stoecker.eu/Haiti-and-domrep/De/tagstats_building_collapsed.html

And it was used to create a Haiti disaster relief map: http://haiti.openstreetmap.nl/

Yes, mapnik treats all building values that are not "no" as buildings and will render them. Please note that the wiki defines building=<building typology=""> but "collapsed" is a building state, not a typology, so I'd consider this "tagging for the renderer" (because although "semantically wrong" it will be displayed "OK").

It might be an alternative to use the well established attribute ruins=yes.