Potatoes can be useful as the first crop on previously uncultivated ground, but probably not for the reason you are hoping.
The main benefit is that if you grow them the traditional way in earthed up rows, you get to dig most of the ground three (or maybe four) times in the growing season while still getting a crop: once when you plant them, once or twice when you earth them up to form the rows, and again when you harvest them.
The leaf cover is also dense enough to suppress annual weeds, if they grow well.
Leaving the potatoes "for biomass" without harvesting them is a bad idea. Unless your winter climate is very severe they won't decompose, they will just grow again next year. Like other plants in the same family (e.g. tomatoes) they are very susceptible to virus diseases which will build up in the soil.
Trying to grow potatoes sold as food may not be a good idea. You probably don't know what variety they are (early, maincrop or late) and potatoes sold all the year round in supermarkets may be imported and not grow well in your climate. They may have been treated with growth inhibitor while being stored as well.
I can't imagine how harvesting potatoes grown around tree seedlings would be good for the trees - the trees don't want their roots disturbed.