Yes. Though the choice of colors and charges was almost always influenced by their lord and their alliances. Often if a coat wasn't chosen, it was differenced from a father-in-law, or an overlord. The first type of heraldry is vary basic colors in some geometric pattern (two colors only, usually) so the knights might choose the same colors as their lord (Roderick of Salisbury uses the same colors as King Arthur, note). As animals and other complex charges were used, these acquired political meaning: for example the eagle = the Roman/German Empire; the lion = England, Anjou, the Welfs; the Lily = France.