Yes, it should work. However, I had the same issue with .user.ini files not setting php_value's recursively. According to official (and short) documentation on php.net they should work recursively (as .htaccess did):
PHP scans for INI files in each directory, starting with the directory
of the requested PHP file, and working its way up to the current
document root (as set in $_SERVER['DOCUMENT_ROOT']).
In case the PHP file is outside the document root, only its directory is scanned.
What I have found out is that Apache configuration had one trailing slash too much which caused .user.ini files not to work recursively.
Take a look at your phpinfo(), specifically SCRIPT_FILENAME variable. Notice two slashes - where should be just one:
$_SERVER['SCRIPT_FILENAME'] = //home/site/public_html/phpnfo.php
The reason for this was coming from apache config, which contained one trailing slash too much.
<IfModule !mod_php5.c>
<FilesMatch \.php$>
SetHandler "proxy:unix:/var/lib/php/php-fpm.sockets/site.sock|fcgi://localhost/"
</FilesMatch>
DirectoryIndex index.php index.html index.htm
</IfModule>
Apache config doesn't include trailing slashes for directories so instead of fcgi://localhost/ this should be written as fcgi://localhost like this:
<IfModule !mod_php5.c>
<FilesMatch \.php$>
SetHandler "proxy:unix:/var/lib/php/php-fpm.sockets/site.sock|fcgi://localhost"
</FilesMatch>
DirectoryIndex index.php index.html index.htm
</IfModule>
After change, restart Apache/php-fpm and you are set.
Update: As it turns out, trailing slash errors in Apache config are still common thing and can lead to different errors and bad php practices (eg set in DocumentRoot /var/www/web/ ).
