I don't think he's ever run a pure 4-3 but I don't think that's necessarily the answer, either. First and foremost, it changes your entire defensive front seven recruiting strategy and you may not get the payoff you're looking for.
In a 3-4 over/under, the lineup is typically a big nose (300+ pounds, preferably 330+) with a couple of DE/T combo players who go 270 or so. Then the LB corps usually is a Mike (even though the LB group is even-numbered) in the 240-250-pound range, a Will at around 230, and then you have the OLB components. The SLB is rarely on the field, because he's the first guy off when the nickel comes on. The other side is the Jack.
What Alabama has been doing, when it goes to nickel, has been to remove the SLB, put the Jack down at end and go to a four-man, shaded front, with the nose still right over center or in the strongside A-gap. The LBs then typically shade to the weakside a bit. When Alabama started going really big at the SLB position, what started happening is that Alabama also took one of the DEs off the field and moved the SLB down to end, so the alignment looked like this: SLB-NT-WDE-Jack. Alabama plays its base defense -- I'm just taking a semi-wild guess here -- about 10 percent of the time nowadays. Alabama is almost always in a 4-2-5, 3-3-5 or 3-2-6 setup.
What makes this different from the traditional 4-3 is the linebackers in a 4-3 usually have a Mike going around 240 flanked by OLBs in the 210-to-220-pound range. When the nickel comes on, they drop one of the OLBs, then drop the other one in dime so you end up with a 4-1-6, which Alabama runs sometimes (typically with the dime walked up into a LB slot; this was the defense Alabama used almost exclusively against Auburn in 2009 with Ali Sharrief basically playing LB).
Tennessee changed from a 3-4 over/under to a 4-3 this year and you saw what happened. Daniel McCullers was rendered pretty much ineffective, because they were asking him to attack rather than mush and he didn't have the feet for it. In addition, Tennessee's OLBs were too big to drop back into the WLB and SLB slots, and when UT lost Curt Maggitt the wheels came off. It takes about 2-3 years to make that transition.
The intermediate step between these two is the 3-3-5 base that Joe Kines used -- you basically get the line of a 3-4 with the linebackers from a 4-3; i.e., smaller all over -- except Kines was also resurrecting the old Miami opposite-shoulder, inside-out philosophy, where everything got funneled outside and the defense used superior speed to make the play. That's why Alabama's OLBs were Terrence Jones (210 pounds) and Demarcus Waldrop (200); they were basically safeties. Kines used a big nose who had two-gap responsibilities, stuck a big Mike (Matt Collins that last year) behind him and then funneled everything out to the edges. When Saban got here, Collins went to DE and only got about a dozen snaps his senior year, because he didn't fit the new scheme. The Mike in Saban's defense is asked to do a million different things. The other big change were Keith Saunders and Brandon Fanney going from tackle to outside linebacker. Eryk Anders, if you remember, was going to be a tackle (!) in Kines' defense.
It can be easy to swap between the 3-4 and the 3-3-5, depending on what the makeup of your outside positions look like. Oklahoma was able to flex between the two all year long, particularly after they lost Corey Nelson at midseason. But that was because their outside personnel had been scaled down to keep up with the outside speed of Big 12 offenses.
Alabama's scheme issue here is that the defense is slow on the corners. The Jacks and ends struggle setting the edge because the mush technique makes them vulnerable to getting zoned on the play. Unfortunately, you either have to recruit a guy for a specific situation, and not play him when the situation isn't there, or you have to sort of restructure the philosophy up front.