Despite what you've been told, YES YOU CAN.
I Installed php 7 with homebrew What is happening is that your Apache conf is still loading php5 as mod_php when you click the "enable php"
go to /Library/server/web/config/apache2. (Or some thing like that.. This from memory)
sudo vi http.conf. Find the string of lines that start LoadModule. The last one loads php5. If you have the check box unchecked, this line will be commented out.
Add this line beneath (for homebrew... Otherwise find your php7 module):
LoadModule php7_module /usr/local/opt/php70/libexec/apache2/libphp7.so
then go to the bottom of the file and beneath the IfModule php5 block, add your own php7 file handler:
<IfModule php7_module>
AddType application/x-httpd-php .php
<FilesMatch .php$>
SetHandler application/x-httpd-php
</FilesMatch>
<IfModule dir_module>
DirectoryIndex index.php index.html
</IfModule>
</IfModule>
Works for me.
CAVEAT: You WILL need to repeat this after a server upgrade.
I Know that this can be done with a webapp, and that would be the preferred way, but I haven't figured out how yet. Perhaps the people that said no, and that server offers no control can figure it out and help us. Meanwhile, enjoy php 7!!!
I also load the opcache and memcached. Wordpress flies.
cheers!