Is it possible to select multiple coded values in a domain field?

No, it is not possible to select multiple coded values in a domain field in ArcMap. This is also a limitation in ArcGIS Online.

The Collector for ArcGIS app supports drop-downs through the use of domains, but currently only allows for a standard single-selection drop-down in the app. An idea has been suggested for this functionality in ArcGIS Ideas: Add multi-select to Collector for ArcGIS drop-downs.

Note:
The functionalities of ArcGIS Collector, ArcGIS Explorer, and ArcGIS Tracker are now available in ArcGIS Field Maps. There are no new capabilities planned for these apps—all future updates will be focused on Field Maps. Migration is recommended. See ArcGIS Blog: Migrate to Field Maps for more information.

However, this functionality is currently available in Survey123 for ArcGIS, where the multi-select is stored as comma delimited text in a resulting feature layer, as explained in the following help page: Multiple choice questions (select_multiple).