Yeah, of course you can. The reason I did a structure like I did is because I started with our old djangotest.zip file which was originally created with like django 1.2 or something ancient, and adapted it to work with the newest django 1.10 that I installed. I'm guessing that's how the django-admin startproject command did things back then, but you're right that command has a very different structure in the latest version.
Using python 3.6 and django 1.10 on my home computer I created a project called hello which looks like this
/hello/
/db.sqlite3
/manage.py
/hello/
/__init__.py
/wsgi.py
/settings.py
/urls.py
Obviously it doesn't work, as you found out already, if you just upload it like that. So we need to make a few changes. The most important things are the .htaccess to force django to process the files, and the .wsgi file that ties it all together. So on the server it looks like this so far:
/public_html/
/db.sqlite3
/.htaccess
/hello/
/__init__.py
/dispatch.wsgi <----- simply wsgi.py renamed
/settings.py
/urls.py
And the code for the .htaccess is this
RewriteEngine On
RewriteBase /
RewriteRule ^(media/.*)$ - [L]
RewriteRule ^(admin_media/.*)$ - [L]
RewriteRule ^(hello/dispatch\.wsgi/.*)$ - [L]
RewriteRule ^(.*)$ hello/dispatch.wsgi/$1 [QSA,PT,L]
Obviously, the last two lines replace "hello" with whatever the name of your project is.
This still won't work though because the wsgi.py/dispatch.wsgi file doesn't have the paths correct for running on the production server yet. Here is what django-admin created
import os
from django.core.wsgi import get_wsgi_application
os.environ.setdefault("DJANGO_SETTINGS_MODULE", "hello.settings")
application = get_wsgi_application()
This is what I changed it to which works both locally and on Tommy
import os, sys
# edit your username below
sys.path.append("/home/krydos1/public_html")
from django.core.wsgi import get_wsgi_application
os.environ['DJANGO_SETTINGS_MODULE'] = 'hello.settings'
application = get_wsgi_application()
Now, when you make a change to wsgi.py locally also copy it to dispatch.wsgi before you upload it.
Here is my test case with the django project running on the root of the domain (instead of in a folder like on my main account).
http://krydos1.heliohost.org/