One thing to consider when training in more than one martial art simultaneously is the possibility of reducing your ability to really learn and absorb each martial art effectively. I trained in a very "street effective" martial art for several years prior to starting aikido, and can tell you that aikido is also very applicable to self defense. As someone said above, it can depend not only on your instructor, but also how you approach your training and view the art. After more than fifteen years in the martial arts, I can tell you that the most effective things I learned about self defense are mental, not physical. These are such things as awareness of yourself and your surroundings and remaining calm and centered in any situation. Although it can take longer to be able to effectively apply physical aikido techniques, you should be able to learn and apply the mental aspects from aikido as soon as in any other art.
I train in Aikikai style, so I am not as familiar with Yoshinkan, but I have heard that it is extremelly effective from a self defense perspective (why else would so many Japanese police oficers train in it?). For what it's worth I would suggest training only in aikido for a while longer before you try to train in another art as well.