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Bruce did a great job answering. Let me just point out something obvious in the section that when Paul uses this analogy he is comparing Hagar to present Jerusalem for a reason because they are under bondage.
The answer to the title of your post is an obvious "Yes", the Judaizers fundamentally missed the purpose of not only the Abrahamic Covenant but the Mosaic Law as well. As Bruce noted, they believed they could live by them but, as Paul notes, anyone who lives by them is cursed when he breaks one portion of it.
Thus, the Jews in essence had walked outside of both the Mosaic Law and the Abrahamic Covenant and were living according to the flesh. They were externally in the CoG but they had completely missed that the types and shadows in its administration were meant to direct them, in faith, to its true substance - Christ.
Remember, the Law could not annul the Abrahamic Covenant. O. Palmer Robertson's book on the Covenant is excellent as it shows an expansion of the CoG as one administration subsumes the previous. It's not as if the Abrahamic Covenant took a break during the administration of the Mosaic Covenant. The Law was added for a gracious purpose. God never considered some crass, faithless offering of a sheep to be the thing that took away sin but it was a sign that was to direct the attention of the believer to the perfect Sacrifice. Abel understood this well before this process was codified.
I agree with Bruce that to push the "re-publication of the CoW" too hard is to miss an important teleological aspect of the Mosaic Covenant. Of course you're going to have reprobate minds treat the administration like a CoW but that doesn't make it a CoW. This is where I think some folks fundamentally miss Paul's argument about the Law and how he is dealing (especially in the passage cited) with a mind set on the flesh and how it's going to perceive the Law: thunder, lightning, with no desire to truly approach it. Instead of approaching it, then, in faith because Christ is the only way to approach it, the unbeliever in the CoG actually shuts his eyes, stays in the place of threatening, and pretends he's not there anymore but fashions a golden calf and calls it true worship.
Hence it is that Ishmael and the "present Jerusalem" were figuratively linked because Ishmael had persecuted Isaac due to his pride in his firstborn status and taking stock in the flesh and the present Jerusalem that is still taking stock in the flesh and missed the entire purpose of the Mosaic Law that testified to Christ. David understood this in Psalm 51. Ishmael and present-day Jerusalem were both under the CoG under differing administrations but both ignored what the administrations pointed to (Christ) and were still in bondage because they refused to have faith.
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