Depending on the terrain you will not have any problems going thru dirt tracks.

Every year here we have our personal Castillian 'Roubaix' (cobbles included). Take a look.

GP Canal de Castilla 2015

100 miles over tarmac, dirt and cobbles. No MTB needed, this year someone appeared with a CX bike but mainly people went with road bikes and 25-28c tires.

700x28c tires are ideal for such terrain. Forget using wimpy 23c ones.