Map Services will work just as well as Feature Services to be able to query that data:
"The following layers are searchable with Query capability enabled:
However if the "SHAPE" field is turned off in the layer before publishing then there will be issues with this search functionality. If the "SHAPE" field has been turned off then the layer may still be able to be queried however it will not zoom to the layer or open the popup related to the item. This is expected behavior.
We have a built in function with our analyzation before publishing that will warn the user regarding this:
24048: Shape field is not visible: In order to properly draw queried map features it is required tha...
We also have a bug related to moving around the shape fields and how it can corrupt the ability to perform popups.
At the end of the day, when it comes to the "SHAPE" field do not turn this off before publishing, make sure this field stays on.
Regarding the format, stray away from rearranging or turning off the "SHAPE", "Shape.STArea()", and "Shape.STLength()" fields from their original format or it could result in the same behavior or corruption.
The "OBJECTID", "SHAPE", "Shape.STArea()", and "Shape.STLength()" fields are hidden by default when adding the item to an ArcGIS Online or Portal Map Viewer.
No matter what fields can be turned off using one of our client applications with the configure popups in the Map Viewer or using one of the Widgets in Web AppBuilder such as the Attribute Table or Smart Editor.
Please let me know if you have any questions!