Copy Remote Database MongoDB
The docs for MongoDB discuss the behavior of copyDatabase in detail:
  http://docs.mongodb.org/manual/reference/method/db.copyDatabase/#behavior

Specifically, copyDatabase reads the data from the source DB the same way something like a backup or full collection query would read it - that means that it may impact the performance of that DB (for example, by bringing more data into RAM which may displace some other data) but the impact would be about the same as running mongodump on that DB.

The docs do explicitly mention that the copied database does not get locked.

If you are running a replica set, you can copyDatabase from a secondary node