Question is self explaining I guess..I've just another regular webserver & I'm really eager to try Phalcon? I'm not sure webhosts allow you to install PHP extensions..
Most webhosts probably would not allow you to install Phalcon, shared hostings aren't good options for high-traffic websites, you can ask them about that or try any of these hosting providers: https://phalcon.io/en/hosting
Sometimes hosts allow you to do that (ie, Site5) but I guess you will have to ask the tech support first if this is supported at all (they will tell you to use either a custom php.ini or rebuild the PHP).
But yes, I would suggest to order a VPS or a dedicated server — this is usually a much better option.
Even if he goes with a VPS or Dedicated. If he gets cPanel it does not support Perl Threads to install Phalcon. So I would make sure with the hosting company before you spend your money on VPS or Dedicated.
I asked my existing host, so no..so I there would be another hit on my wallet :) pretty soon, but I'll try it on dev VM's as I seriously wanted to benchmark those request/per sec of Phalcon..to see if it'll go in my next mobile API