Is this possible to do with ACF? Yes it is.
Will it be difficult? Yes.
You will need to build a page of some kind that will show all of the listings submitted by each user. This can be done in various ways using WP. For example users could be set up as a Taxonomy and then you could use the taxonomy archive template to show the list. This could also be done with a CPT where each user has a post and then listing are child posts of their main post. Their are probably other ways this can be done.
With this listing page in place you could add an acf_form() to the page that would create a new post based on how you decide to build the system for storing the listings discussed above.
