Hi javiern,
It is possible to expand the datastore without powering off your virtual machines.
As you mentioned, the first step would be to add the disk from Dell Open Manage.
Then find the below article, which explains how to extend the local datastore.
http://www.virtadmin.com/how-to-grow-a-local-vmfs-datastore/
The official documentation can be found below.
Cheers,
Adil Arif