Email Users supports sending email to users either individually (pick one or more users as recipients), Groups (which are based on WordPress Roles and Capabilities) – for example, the WordPress “Editor” role can be assigned to a user and if you choose to send to the Group “Editor”, any user assigned the Editor role will receive it (unless they disable receiving email).
The ability to send email is based on the capabilities which Email Users defines, a description of which can be found at the bottom of the Email Users settings page.
If you can define a role for your custom group and and assign a number of users that role then you will be able to use the existing Send to Group functionality to send to your users. There are quite a few plugins which allow role and capability management, Email Users does offer that capability but will make use of it when defined.
The other option is to use the relatively new Meta filter capability. You can define custom filters to target selected users based on user meta data (user specific data stored in the User Meta table). If your custom group information could be stored as user meta data instead of a separate table, it would be fairly easy to achieve what you want to do.
Here is a post on my web site which goes into some details on using Custom Groups.