You've already got some definitive responses here from Mica, but I thought I'd ring in with a few thoughts.
First, I would concur that you should be able to substitute DiMarzios (or any other pickup) in place of the OEM Alembic pickups, and the only way that you can decide whether you like the change or not is to try it.
You'll need to either feel comfortable attacking the installation yourself or have an adventurous tech to go after this. The actual pickup connections are no big deal (the new pickup connections replace the old), but everything they attach to internally in the control cavity will be different than pretty much every guitar out there. There will be connectors (which you could just lop off, but wouldn't that be a shame?), unusual EQ boards, and a lot of wiring.
My experience is mostly with Series basses, and I think the guitar pickups are much less radical than the SC-1 pickups. Alembic is like nothing else out there - they use a very weak magnet and very little wiring on the coil, which has the result of a very, very low output pickup with only a fraction of the normal output. There's very specific reasons for this. The lower strength magnet reduces magnetic drag on the string which gives greater sustain and much purer harmonics. Less wire on the coil means less resistance which means better highs. It also means less inductance in the coil which also creates a different frequency response (the coil inductance is a big factor in the distinctive EQ hump of most pickups). If you took this wimpy output out passively to the amp, you wouldn't be able to drive the amp to full output and would probably suffer a lot of noise problems. So, the internal preamps buffer and boost the signal to normal (and super-normal) levels. That means the internal preamps of a Series bass will be set with high gain than the sort of active EQ circuits designed to work with conventional passive pickups.
I'll add incidentally, that the low magnet strength and low output transducer coil are also the EMG design principle, and they include the preamp inside the pickup to avoid noise problems and isolate the EQ boards. EMG also is a hum-cancelling design inside the potted case, so even the Strat-sized EMGs are humbuckers (that's why they hum less).
If the DiMarzios are high output pickups, then you may well find that they will overdrive the front end of the EQ circuit. You can reduce the pickup output level with a resistor, but this may cause additional tonal changes. If the input level is the problem, you really want to fix that in the EQ board, but that means you'd have to puzzle out the design of that PCB and figure out the appropriate component changes. This may not be a problem - the Series pickups are very unusual, and, from the general flow of discussions around here, it doesn't sound like the other bass pickups (and perhaps the guitar pickups) are as low output.
The unusual pickup design is definitely part of the Alembic Sound. If you take a DiMarzio, Duncan, or Gibson pickup, they all have similar magnetic field strength and coil winding. Different choices in construction (diameter of the wire or magnet composition) will yield different tones, but the magnetic field that the string is sitting in is pretty similar for any of these. The Alembic design sees the string in a different way - whether that's good or not is totally subjective and definitely getting in to the mystical/voodoo zone.
Finding an alternate rotary selector switch may be problematic. If you wanted a 5-position switch that selected from 5 different inputs it would be no big deal, but when you want some of those positions to be combinations of other inputs, it gets complicated quick in the switch internals. The manufacturers will build anything you want if you want thousands of them (which is why 3- and 5-position blade switches and crazy PRS pickup selector switches can exist) but if you want one, you'll probably be in for a battle.
You didn't say it in the thread directly, but if what you were looking for was the sound of the Alembic woods and construction with more traditional electronics, I certainly can understand that. If I were going to try this, I would probably think about removing and setting aside the factory pickups and EQ and building up a second set of electronics. When you're talking about mods on a Tribute, you're way past the money is no object stage, and I suspect the replacement cost of just the Tribute electronics will exceed the cost of most whole guitars. If you try to graft more traditional electronics onto your Tribute EQ boards, you may find that the changes are too complicated to work out and not easily reversed. If you later decide to sell this guitar, you'll probably find that you'll take a truly horrendous hit on the resale value if you can't reverse your changes.
Good luck,
David Fung