Yes, it does, probably you're inspecting the wrong param, it will call the same webhook, first remember you set the webhook by doing:
https://api.telegram.org/bot<BOT_TOKEN>/setWebhook?url=<YOUR_URL>
and like you mentioned, you need to enable /setinline through BotFather, then it will call your endpoint with a message with the following body:
{
"query":"tex",
"from": {
"username":"user",
"first_name":"firstname",
"last_name":"lastname",
"id": 8888888,
"language_code":"en-US"},
"id":"7777777",
"offset":""
}
Remember it will call your endpoint on key-up you may receive a ton of request.