Is a free site & subdomain searchable? Or are you limited to having to enter the full address (therefore limited use for new custom)??

Hi, I'm thinking of using yola's free site building & subdomain, (im starting a business & have been out of work for 2 years so im very poor!).
They suggest tips for optimising your site for a local search in the tutorials, which sounds great.
BUT, if you just do the free subdomain is your site searchable? either by someone searching under your business name or making a generic search for your type of service in your area?
I know of someone who has done this free yola subdomain site & however I search I cannot find it unless I put in the full address in the address bar.

This would mean that the site has limited benefit to those who have the address already....not really attracting new customers.
Am I right or have I missed something?!