Maybe...something could be in either high or low demand and the cost could be either high or low for both. For example, a Ferrari is in low demand yet commands a high price. The reason for the low demand is because the price is high and the price is high because supply is low.
Cost/price is more relevant to the ratio or relationship between demand and supply with the basic principle of supply and demand's affect on price being that price changes depending upon changes in supply and/or demand. Another way to put it - compare two items that can be substitutes - a McDondald's hamburger and a Peter Luger hamburger. Both are on the face the same product. The mcD's hamburger price is about $1, the Peter Luger hamburger price is about $25 - by your logic, the cost/price of the Luger-burger should translate into high demand. However, McDonalds sells a lot more of the $1 burgers than Lugers sells of the $25 burger (meaning demand is higher for the low cost burger). If McD's raises their price to $1.25, all else being equal, demand goes down - higher price less demand. However, if McD's raises their price to $1.10 but Luger's raises their price to $27, assuming static demand for hamburgers, the demand for McD's will increase while that for Lugers will decrease. But if someone comes in, say BK and offers a burger similar to McD's for $1, McD's demand will go down even though their $1.25 price did not change.