Now this may be interpreted allegorically: these women are two covenants. One is from Mount Sinai, bearing children for slavery; she is Hagar. (Gal 4:24)Just a couple of quick notes on the text...
1) Paul does not say that this is the proper interpretation of the story. Instead he says that it may be interpreted allegorically. What he means is that he is taking a narrative from the Old Testament and using it to form a parable of sorts, in order to make his point. This is not an appeal to Scripture proving his point...he has already done that. (See Gal 3:1-4:20) Instead he uses it only as a device to illustrate his point.
2) Paul is not using a new interpretive principle here. In fact, he is not using any interpretive principles since he does not mean to interpret the text in any way. He provides the history, declares that he is going to use it allegorically, and then illustrates his main point by his allegory.
3) Allegory is a valid way to interpret Scripture, but only when warranted by the text by it's genre or an explicit statement. When Jesus says that the Kingdom is like_____, allegory is expected.
4) The point of the illustration is that the law, or the old covenant, produces slaves, while the Gospel, or the new covenant, produces heirs.
5) This is a great way to illustrate a point in preaching, so long as we make it clear that this is not an interpretive principle, for a couple of reasons. First, it keeps the preacher in Scripture in his studies and preaching. Second, it keeps the hearer focused on Scripture and shows them the preacher's emphasis on Scripture.
6) This is not the only, or even the best, way to illustrate a point in any given situation. Obviously, for Paul, this was the best way given the situation he found himself in, and given the background of the Galatians in the law.
7) But it is a way to illustrate the point that can be beneficial. For example, consider Paul's argument in Galatians...Abraham was justified by faith alone, God made promises to Abraham that were not based on the law, and Christ is the fulfillment of those promises. The readers of the letter are already thinking about Abraham's life. So it is very appropriate that Paul would allegorize this aspect of the story of Abraham to make his point. The Galatians would have understood that he was not interpreting, but illustrating what he had already said in the previous parts of the letter.