Is it possible to restore mongodb after db.dropDatabase() by replacing the contents of folder /data/db with older backup?
Yes and no. Yes, you can do this and your DB is at same state what it was when you took that backup especially if you used journaling. This means of course that everything that you did (changes to the DB) after backup disappears.
No part is more like that if you do your backup this way, 
you should use filesystem snapshots or you should other way prevent disk writing during the copy process.