It should work, however http://nginx.org/en/docs/http/ngx_http_core_module.html#alias says:
When location matches the last part of the directive’s value: it is better to use the root directive instead:
which would yield:
server {
listen 8080;
server_name www.mysite.com mysite.com;
error_log /home/www-data/logs/nginx_www.error.log;
error_page 404 /404.html;
location /public/doc/ {
autoindex on;
root /home/www-data/mysite;
}
location = /404.html {
root /home/www-data/mysite/static/html;
}
}