Yes, that applies to pine tar too. People ask this question all the time about all kinds of ingredients -- if I put X in my soap, will its magical benefits survive? There's no way to know without doing a scientific study. A lot of the claims you hear about these additives are purely wishful thinking without a gram of facts to support these claims.
Scientific studies have not shown pine tar itself to be effective for treating skin problems, even though it has been used for a long time as a folk remedy, whether used directly or added to soap. I make pine tar soap as well as neem oil soap, but I don't tout either one as doing anything more than getting a person clean. It's soap. It cleans. That's it.
I get the feeling you've assumed a pine tar or pine oil soap will actually be effective against eczema. If I've learned anything here at SMF with medical professionals and people with skin problems, it's that no one ingredient will 100% help everyone who has eczema, dermatitis, psoriaisis, acne, or other skin problems. There are many different triggers for these problems, so no one special ingredient will be a cure-all. Probably the best place to start finding some relief is using is a simple, mild bath soap with low to moderate superfat, no color, no fragrance, and no "curative" ingredients.