The title is saying everything. Assume that you have a sharded MongoDB environment and the user provide a query, which doesn't contain the shard key. What is the actual performance of the query? What happens in the background?
The performance depends on any number of factors however, the default action of MongoDB in this case is to do a global scatter and gather operation whereby it will send the query to all shards and then merge duplicates to give you an end result.
Returning to the performance, it normally depends upon the indexes on each shard and the isolated optimisation of their data sets and how much range of a dataset they hold.
However processing is parallel in sharding which means they all get the query and the "master" mongod will just merge as they come in, so the performance shouldn't be: go to shard 1, get it, then shard 2; instead it should be: go to all shards, each shard return its results and the master merges and returns.
Here is a good presentation (with nice pictures) on exactly how queries with sharding work in certain situations: http://www.slideshare.net/mongodb/how-queries-work-with-sharding