Yes. As you know, WordPress is perfect website design software and more than 80% websites are based on WordPress software. WordPress application can run in any servers and exhaust very few resources.
Cheap web hosting providers normally provide you cpanel or plesk control panel. It is very easy to install WordPress in any Cpanel or Plesk control panel.
WordPress is lightweight when it’s initially installed, so most cheap hosting accounts will cope just fine, providing your plan allows you to create the database that WordPress needs to function.
If your WordPress site grows and becomes very resource-intensive, your host may ask you to upgrade to a more expensive plan so that it doesn’t negatively impact on other customers.