In the text for the Improved Pact Weapon eldritch invocation (XGtE, p. 57), it says:
In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.
In the case of +X weapons or weapons like the Sun Blade (DMG, p. 205), whose effect specifies a +2 to attack and damage rolls, the rule is pretty clear: Take the weapon's effect; it does not stack with the invocation's +1.
But, how would this apply to a weapon such as the Sword of Wounding (DMG, p. 207), which does not confer a bonus to attack or damage rolls but rather has an unrelated effect?
Hit points lost to this weapon's damage can be regained only through a short or long rest, rather than by regeneration, magic, or any other means.
Once per turn, when you hit a creature with an attack using this magic weapon, you can wound the target. At the start of each of the wounded creature's turns, it takes 1d4 necrotic damage for each time you've wounded it, and it can then make a DC 15 Constitution saving throw, ending the effect of all such wounds on itself on a success. Alternatively, the wounded creature, or a creature within 5 feet of it, can use an action to make a DC 15 Wisdom (Medicine) check, ending the effect of such wounds on it on a success.
Would Improved Pact Weapon effectively grant me a Sword of Wounding +1, or would I still have a standard Sword of Wounding?