Addresses in Japan pose a special problem for both OpenStreetMap and OsmAnd. They do not use an actual 'street' address, since many of their streets are not named. The address you gave is broken down as:
Tokyo: the city name
Asakusa: section of the city
2 Chome: neighborhood (maybe 10-30 blocks in a roughly square area)
1: a single block within the neighborhood (the number is arbitrarily assigned, no specific order)
1: the building number (assigned when the first building was build on this block,
assigned in the order in which buildings were build; so #1 might be next to #5 and #27, and #2 might be on the other side of the block)
There is no relation between a building's address and the street where it is located. I checked Asakusa on OSM, it looks like all of the buildings have been mapped, but NOT the Chome or blocks. The buildings in OSM are NOT tagged with their addresses. Still a lot of work to be done in Tokyo to map it correctly in OSM.
OsmAnd should be able to get you close to a location, only if the Chome were tagged in OSM as suburbs or neighborhoods, and the building number was tagged in its "name" tag. So the problem is with the OSM data, not OsmAnd.
Hope this explanation helps,
Dan