Generally speaking, countries with PR systems do have more women in Parliament than countries that don't. Being confident that this is cause and effect is a different matter. Maybe it's just that the countries are different, that their whole political culture is different.
Ireland, I must say, has always done very poorly on this criterion. At the last election, we introduced candidate gender quotas. That did have the effect of increasing the proportion of women to 22%, which is the highest for Ireland, but Ireland is not a great exemplar on this point. Again, I think it's one of those things that is not really determined centrally by the electoral system.
To go back to something I said before about open-list and closed-list PR systems, with a closed-list system the party in effect picks the MPs. The party can put a lot of women at the top of the list, or people from ethnic minorities, and in that way really engineer the composition of its parliamentary group. It can be used for that purpose, but at the cost of freezing the voter out of the decision-making process.