Yes it is feasible to get the item id from the return result. You just need to add the
itemidin the field projection. Please see below the updated Rest API
I did a small test with the home item and the result are shown below (which returns the item id from where it got the result)
"Title": "Sitecore Experience Platform"
More information can be obtained from the Sitecore Documentation - The ItemService.
In the section ItemModel return values, it shows what are the different values that it returns. You just need to specify them in the field projection.