Yes, a player still triggers their house ability when they would gain the Sovereign token, even if they already have it.

This is stated in the rulebook:

• "Each house tile has an ability that is triggered whenever you gain the Sovereign token (even if you already have it). Typically this will happen by gaining a card from Luna, but it also applies to any card ability from which you would gain the Sovereign token, as well as rolling Luna on the Rising die. First gain the Sovereign token, then trigger the ability. These house abilities must be resolved if possible."
  (Page 5)

This means the house ability is always triggered when you "gain" the Sovereign token, regardless of whether you already possess it.

Source: page 5

Source: Core Rulebook (pp. 1, 5, 7)