Mongo Scaling - Too Many Connections - Linear Horizontal Scaling with 100s of App Servers
The hard connection limit was actually 20,000 but it was removed in version 2.6 and you are now only limited by memory or open file descriptors (whichever you run out of first).  That being said, with connections running into the thousands, even if you can manage it you will be using a lot of memory (1MB per connection for the stack).

At that point you start to evaluate other options for mongos deployment.  You can have a dedicated set of mongos hosts and take advantage of some of the nice HA options built into the drivers and pass in an list of possible mongos processes to use.  If you are concerned about latency, you could potentially collocate (some of) the mongos processes on your shard hosts.

Basically you've started to hit the number of nodes where you are into more advanced design decisions and it really depends on several factors as to what is right for you now, and what is right for you in the future.  If you have some money to throw at it, this is perfect fodder for the type of consulting MongoDB offer (disclosure: I was once one of the people delivering such consulting).  If not, you are asking the right questions, so keep an eye on resource utilisation and see what makes sense for your deployment as you grow.