I am wondering if [it] is necessary [to have these files?]
No, it isn't strictly necessary to have any particular files on a web server, including any "default" index pages (the ones you listed).
[W]hat happens if there is no such file name[?]
The server will generally do one of five things:
dump a directory list of the files that are available (assuming a default index page does not exist or isn't configured).
block access to the requested resource directory (if specified in the server settings - usually via a 403 Forbidden status code).
serve a alternate index page (if specified in the server settings).
return a 404 status code ("Not Found") (unlikely, but possible).
redirect a user to a valid resource (if specified in the server settings)
My first guess is that the server would display a complete listing of the site's project directory.
This is the default on a number of web servers, assuming that a directory/default index page combination is requested, and the default index page does not exist.
Is there any other outcome except a display of the site's full directory?
Yes, see above.
Is there a possible way to avoid this without naming a default page file name?
Yes, configure your server to do one of the things listed above (other than dump a directory listing).
Does [not having a default index page result] in a loss of SEO ranking?
If you are blocking access to the directory via the server (with a 403 Forbidden) or the server returns a 404, search engines can't crawl your content. Google will definitely not direct people to pages with blocked content (403) or items it thinks don't exist (404).
Redirection or serving another file might cause a crawler to index something unrelated to that directory (though this may not be true depending on what you redirect to). This may affect SEO.
Dumping a directory may or may not help SEO depending on what is dumped and how Google might rank that content.
I am not sure if Google or any other search engine has a direct penalty for a lack of default index pages, but I can imagine they might interpret it in a manner that might negatively impact SEO.