In terms of metaphor/allegory, absolutely. There are many parallels between the story of the Levite and his Concubine and the story of Saul:
- Saul/Concubine both from Gibea
- Saul/remnant of Benjamin hiding on rock of rimmon with 600 men
- The cutting of the two oxen/concubine and distribution to Israel to draw them into war
- Jabesh-Gilead destroyed in the levite story but saved by Saul
This parallel has been written about in many papers.
However there is not a clear parallel throughout the entire narrative, it's like bits and pieces of Saul's early reign are being described but in a mish-mash, sometimes the story parallels it, other times it contrasts, and there is not a consistent mapping of metaphors from Saul to the Levite.
What this suggests (to me) is that both the stories of Saul and the levitical stories are using a common metaphorical language. E.g. "the 600 men" is a general symbol for "the chosen men" in Ex 14.7, Judg 18.11, 1 Sam 23.13, 2 Sam 15.8. The rock of rimmon is a general symbol for sanctuary (on the rock, so Christ), so both the remnant of Benjamin on that rock are saved when the hosts of Israel ("who come together as 'one man'") have compassion on them but also Saul and his men are delivered from the Phillistines (by Jonathan) when they are on the same rock.
Thus there are parallels with the story of Saul as well as with the story of Lot and other stories because all these are using the same metaphorical dictionary and are prophecies of slightly different aspects of the same prophetic events, which in Christian Hermeneutics would be Christ's life.
In the specific case of the sacrifice of the oxen, there are some things to consider.
In traditional covenants the animal is not cut into a dozen pieces but it is cut in two pieces - e.g. Gen 15.10. Then the swearers to the covenant walk between the pieces and swear an imprecation to the effect that let this be their fate if they do not honor the covenant (see Jer. 34.18-19). From the NICOT commentary [N]:
The biblical world offers widespread evidence that animals were
slaughtered in treaty contraction ceremonies. Some of these texts—but
not all of them—suggest that the two parties to the treaty walked
between the rows of freshly killed animal flesh, and in so doing
placed a curse upon themselves if either party should prove disloyal
to the terms of the treaty: May they too be torn apart if they are
responsible in any way for violating the arrangement.15 The most
frequently cited text to support the thesis that the procedures taken
by Abram function as a dramatized curse is a seventeenth-century B.C.
treaty from Alalakh between Yarimlim and Abban. Abban has just given
the city of Alalakh to Yarimlim, the vassal ruler, and to cement that
transaction the text says: “Abban placed himself under oath to
Iarimlim and had cut the neck of a sheep (saying): ‘(Let me so die) if
I take back that which I gave thee!’ ”
Typically in the covenants, it is the greater party that swears the imprecation upon himself not the lesser party. So in the covenant with Abraham, he is put to sleep and God alone walks (as the smoking pot) through the pieces of the animals, thus God alone will be treated like a sacrifice if Abraham breaks the covenant. Thus it is both a prophecy of Christ and an imprecation.
But now with the oxen of Saul, they are cut into a dozen pieces, distributed to Israel, with the imprecation that "this will happen to you if you do not go to war". This is another hint that the unified Israel now typifies God, the greater party in the covenant. The text follows with "Then the dread of the LORD fell upon the people, and they came out as one man." (1 Sam 11.7 ESV). The same language is used with the Levite's sacrifice:
Judges 20.11 [ESV]
So all the men of Israel were gathered against the city, knit together
as one man.
And this phrase "one man" [ish echad] is used three times, in Judges 20.1, 20.8 and 20.11. Moreover when Israel fights, the Hebrew text says "man of Israel" not "men of Israel". Thus the idea is that the sacrifice unites the people into a single man, and in this there is the prophecy of both unification/reconciliation as well as resurrection, as all the various pieces that were distributed are brought back together.
In fact both the story of the Levite and his concubine as well as the story of the first battle of Saul contain the motif of recovering unity from a state of division, and so the division of the concubine/sacrifice is distributed to the divided tribes as a means to get them to unify into a single body, and hidden within that is a prophecy of the resurrection of the bride/sacrifice.
[N] Hamilton, V. P. (1990). The Book of Genesis, Chapters 1–17 (pp. 430–431). Grand Rapids, MI: Wm. B. Eerdmans Publishing Co.