The short answer is yes, if your site was built by someone competent within the last 18 months, it should be mobile friendly.
The longer answer is that it’s not WordPress as such that makes the site mobile friendly, it’s the theme that is used (or a mobile website plugin) that will define whether the site satisfies Googles “mobile friendly” criteria.
The vast majority of WordPress themes that are for sale these days are what is termed “responsive”. This means that the layout of the website changes according to the size of screen that is being used to view it. The advantage of this is that the content remains the right size to be easily read and links easy to click/touch without having to zoom or pinch in/out.
So, if you are looking to build a website (or have your website built) on WordPress today there is no excuse for it to not be mobile friendly. Additionally, it should not cost any more than a website that isn’t mobile friendly. The technology is built in to the theme.
If your website is already on WordPress and was built in the last 18 months or so it should be mobile friendly but you need to check.
If your website is older it is unlikely to be mobile friendly, but you can check by typing the address in on this page https://www.google.co.uk/webmasters/tools/mobile-friendly/
At Orange Pixel al our websites have been built on WordPress and have been responsive for the last two years. If you need help in bringing yours up to date please do get in touch for a quick, no obligation chat to see if we are a good fit for your needs