Setting up a Wordpress XML listener for live updates of posts?

I recently got assigned a task wherein we need to implement a listener for XML on our Wordpress site. The idea is that a third party service will push XML to us the instant there is a new job opening. This XML contains details about the opening. Once we receive this XML via a push, we use the XML to create a new post on the website for the opening.

I am wondering if it is even possible to create a constantly listening service in the background on a Wordpress site, without any users actually visiting the website.

I understand that it is possible to set up listeners in PHP, but the listening would only occur while the web page is actively open, correct? If that specific page is not open by at least 1 person, the pushed XML will never be received?

My second question is, if a POST request (instead of GET) is made to a page (i.e. the XML push), will all the functions on that page be executed regardless? If this is the case then the listener should be relatively easy to implement, as all I would need to do is create a page which listens for and handles the XML. Then instruct the XML push to be sent to that web page. I fear that this is not the case though. If anyone could confirm this for me I would be deeply appreciative.