So, by "FM", I'm assuming you mean Chowning FM, also known as algorithmic FM. Now, yes, this is technically doable in a modular environment. There are several 2-op FM modules around, besides Akemie's Castle which is 4-op, using a NOS Yamaha 4-op chip, of which Yamaha made several variations over the years. All well and good...BUT...
The problem with Chowning FM in the analog domain is that, to get the full advantage of it, you need a buttload of modulator sources. Envelopes (looping and otherwise), LFOs, function generators, etc etc are the real 'meat' behind FM. The Akemie's just allows you to control the different operator and oscillator functions via continuous CVs. But that's where the trouble starts...
Go back over to ALM's site and watch the video on this module. Now, when the user starts adding envelopes to control the operators, listen carefully to what's really going on. Notice that 'stepped' bllggn-ingg-eeng-ingg-type sound as the voltage curve sweeps the operator(s)? This is happening because no matter how smooth you make the incoming voltage changes, the Yamaha YM-series chip is going to reinterpret that in discrete steps. And there's not really any workaround for that; it's simply how the Yamaha digital chips were designed to be used, with what's going on in the Akemie's Castle being a bit of a kludge to get one to 'recognize' CVs...but not necessarily take full advantage of the continuous change in the CVs. Sure, you can get some really complex sounds that way, and the Akemie's makes it easy to get a simulacrum of FM under analog control...but you're still only dealing with a simulation. To see what's really supposed to be going on (and does under the proper digital control in Yamaha's FM implementation), see here: https://en.wikipedia.org/wiki/Frequency_modulation_synthesis (NB: the forum mangled this URL slightly...insert underscores between the last three words). Note the little block diagram in the upper right corner; that shows how each "operator" is configured, as a combination of an oscillator, an envelope generator, and a linear VCA which allows the EG to modulate the outgoing level of the oscillator. This result then passes on to modulate a second, identically-configured operator, and so on.
BUT...reading further in this Wikipedia entry, we find some notes about how Don Buchla's complex oscillators also were designed to make use of FM sound generation techniques. Now, this is where it gets interesting. Assume that, instead of having the Yamaha NOS chip in the Akemie's with its digital translation of analog CV curves, you were to build up the operators as discrete modules. There's actually no reason why you can't...and in fact, doing FM synthesis THIS way eliminates that stepped bllggn-ingg-eeng-ingg, replacing that with the beautiful sweeps of truly analog-controlled FM. And hey, look at what Happy Nerding's got...a discrete module that has the necessary VCA configuration, all ready to go. Just add a VCO and modulator, and there you are!
Naturally, though...there's a downside. Or a few, actually. First of all, such a setup will be a bitch-and-a-half to program and control. You'll be in constant tweak mode until all of the many controls in such a setup are exactly where they should be. And if anything gets knocked ever so slightly out of whack...there goes your sound. So you'd have to take a certain degree of unpredictability into account. Then there's the cost. To do six-op FM (like a DX7, more complex than a 4-op but more nuanced), you would need six VCOs, six envelope generators, and six properly configured linear VCAs, plus the ancillary modules needed to control those and alter their routings (if you want to get that complicated). And that's going to get spendy. Plus, that's also going to get sizable unless you're OK with doing much of this on smaller modules.
Soooooo...if the Akemie's Castle is a bit of a 'kludge' and the real analog implementation is insanely complex, what do you do? There's a few options...
1) Get the Akemie's Castle...knowing that, to take advantage of it to its best potential, you're also going to need a pile of modulation sources...mostly EGs, but some LFOs as well, possibly. Result: modular FM, but not exactly as it could be, with a goodly amount of programming and knob-juggling.
2) DON'T get the Akemie's Castle, but try and implement this purely in the analog domain with VCOs, VCAs, and modulators. Result: real, fully-realized FM in the same sort of modality as Chowning FM, but with the sacrifice of easy control and higher cost. It'll also potentially result in a rather large build.
or, 3) Have a look at Yamaha's new MODX synths. No, they're not modular, I know...but for what this modular build will cost, you can instead get an MODX6 (possibly for less, even), which then gives you 8-op FM (like the FS1R, as well as the FM implementation in the Synclavier). The programming gets much easier since it's then under the synth's microprocessor control. Also, programming one of these is NOT the brain-wrenching chore that programming the early DX and related Yamaha models was back in their day, when you had minimal display feedback and one crappy data slider. Since the MODX is an FM-centric offshoot of the Montage, you now get a full touchscreen and ample real-time controls.
Ultimately, the last option makes the most sense to me. In fact, I'll be picking up one of those MODX6s this coming spring, because even if I have a modular setup, it does what IT does best, and the MODX will do what IT does best, avoiding the headaches of the synth programming equivalent of cramming a square peg in a round hole. And, having used the DX series (and I still have two FB-01s, in fact) and grown to HATEHATEHATE programming them, I can safely say that the MODX kills the crappy interface argument against their FM implementation. It's a very different creature. And that leaves my modular for doing things it's happier with...and that I'm happier with, also!