Under most conditions, it can only help.  Most providers over-stuff their servers to make an extra nickel at the expense of their customer's website performance.  We do not allow more than 300 websites per server which mean there are always plenty of resources available to serve the website.  Combine this with our proprietary PHP environment (a combination of PHP FPM and REDIS and in-house software to accelerate WordPress websites) and you have websites that can easily reach A+s on GTMetrix evaluations - if your code isn't clunky.