Technically NOPE, you don’t need to have a domain name (like mydomain.com) in order to publish or even promote your Clickfunnels’ funnel or landing page, since Clickfunnels automatically assigns you a free subdomain that you can use directly, without the need to any extra configuration.
But taking it from a performance, psychology perspective, People tend to trust domain names (especially short ones) compared to the long domains or free-subdomains.
And if you are one of those focusing on SEO to drive traffic, then a root domain is a MUST.
You can find more insightful information about how a domain name can affect your business on this wiki article by @yassine: