Yes and No.
An Internet connection is mandatory to log in at first run and download the virtual device images. However, a 15 days token is generated after signing in, so it is possible to use Genymotion Desktop offline during 15 days between each connections.
After this time, though, you will have to connect to the Internet so that Genymotion can verify your credentials.
It is possible to extend the token life span by request, but this service is strictly reserved to customers with a paying license.