Yes, it does. It doesn't necessarily make them do a good job, but the same therapist with no personal therapy experience would do a poorer job than when he knows what it's like to be a therapy client.

I would absolutely make undergoing personal therapy a mandatory requirement for getting licensed.

That being said, personal therapy experience, while necessary, is not enough to ensure that the therapist is effective.

First off, there is always a limit of how much one can resolve in therapy. There will always be unresolved deep seated issues, no matter how much therapy one receives. The best the therapist could do after doing some of their own therapy work is simply be aware of those unresolved issues in order to know the limits within which they can work. Therapists are most effective when they work only with those clients with whom they can establish good rapport and good working alliance and only with the problems they feel passionate and most knowledgeable about. But a therapist should know her/himself well enough in order to determine who s/he should and should not be working with and what kind of work s/he should and should not be doing. A personal therapy certainly helps to gain this kind of self-awareness.

Another reason why having a personal therapy experience is not a guarantee that a therapist will do a good job is that many times therapy is not effective at all. More often than not clients, including those who are therapists, see therapists only for the purpose of getting weekly emotional support from someone and also, as a regular routine, just to give themselves an illusion that they are doing the work they are not really doing just because this "thing" is on their schedule. So, just because someone has seen a therapist for some time doesn't necessarily mean they have done some meaningful work.