Basically what X and Inccubus said.
The castle is a "creature of Chaos," as told by Alucard. Now, this line was delivered years before Aria was made, so I don't quite believe the Chaos as Aria describes it was planned out during SotN's creation. That being said, I think the notion of the castle being an extension of Chaos has been around in the canon for some time. Chaos is already a perpetual and fundamental force of nature, physics, and existence. Entropy as the force of decomposition and breakdown over time can and has been easily construed into a parallel of Darkness and death. Since Dracula is undead, he contradicts the "Light" part of existence and by comparison, a part of entropy. He doesn't break down in the conventional sense (but he does, through his cyclic 'deaths'), but in being a sort of paradox of the life cycle, he perpetuates entropy and chaos by his very existence.
Given his powers as Prince of Darkness, controlling Chaos as a force would be easy as sin for him. But like any fundamental force of nature, I don't believe he has complete and utter control over it. Rather, I think that he has enough control over Chaos to grant him extensions and stat boosts, in a sense, to his already-existing powers of Darkness. In this context, I mean that Dracula has powers that - within the CV lore - can be learned by humans. Pyromancy, necromancy, teleportation, shapeshifting, life-draining, umbramancy, etc. etc. are all abilities seen and used by human foes throughout the series. Shaft being a prime example. However, his connection to Chaos amplifies these powers a hundredfold. So, I think Chaos "allows" him certain degrees of control, but being a preternatural force of the universe he can't control it fully. On that tangent of "allowing," I don't know whether to consider Chaos in the CV universe a sentient force or not. We see it in Aria as intelligent, but that could perhaps be chalked up to a core essence of Dracula's power. A guardian of his strength, as it were. I don't quite believe that Aria's Chaos is the Chaos, but rather a manifestation of Dracula's core powers created, perhaps, as a sort of lock and key for the castle.
To add on to the gun metaphor, if the castle is the gun itself, and Dracula is the gunslinger (Hellsing, anyone?), then maybe Chaos could be either the bullets or the firing pin. Without Chaos, Dracula's power is theoretically no greater than that of any human sorcerer. Without Chaos, the Castle as a living entity is nothing more than a structure of wood and stone. In this sense, Chaos is the rug that ties the whole thing together, man. Dracula without Chaos as a conduit is, in my opinion, nothing more than an extremely powerful vampire sorcerer. Chaos is what perpetuates his rebirth cycle. Chaos is what keeps his castle in order (or lack thereof) and the reason it remanifests in a different form each incarnation. I also think that, in regards to the castle's self-destruct button, Dracula has some form of control over the castle's state. IIRC there are hardly any CV games in which Dracula leaves the castle grounds, which (if I am remembering right) could mean that the physical state of the castle is directly correlated to whether or not Dracula's in it. Assuming this is the case, I think that his death and/or leaving of the grounds would most likely trigger its collapse, or at the very least weaken its supernatural abilities (i.e. monsters wouldn't spawn anymore, those that are there would become very weak, and the masters of the various sections would become considerably less formidable), because Dracula is no longer present for the castle and its inhabitants to siphon power from.
I think, really, Dracula is a tap, a font if you will, for Chaos as an entity of Darkness (and perhaps evil as well, in the CV universe anyway) to manifest in places it normally wouldn't. Based on this idea, I think this can explain why Dracula and his fortress are so deeply connected, and why it doesn't crumble in the DCW. Without Dracula on tap, the castle cannot sense whether or not he has been defeated, and thus can't tell itself to self-destruct. I think that this was discovered by the DCW crew (probably Alucard, since based on his "creature of Chaos" line likely knows the nature of the castle, assuming again this long-ass theory is probable), and was thus exploited as Dracula's only true weak point (the source and manifestation of his power is also his greatest weakness, poetic irony, no?) by having Julius isolate Dracula from the castle and cut the two off from one another and only then kill him. Without the castle to perpetuate his cycle and rebirth, and without Dracula to give the castle its true power, his cycle was ended.
I think, in considerable sum, that Dracula and his castle are mutually dependent, and in a very elaborate sense one and the same. The two together, in my opinion, form a sort of paradox, in which one cannot fully function without the other, but also whose powers stem from the other. Castlevania gets its power by Dracula's presence/existence, and Dracula has access to his full power by being within the realm of Castlevania (since it IS a pocket dimension of sorts). One cannot exist entirely without the other, but the two were also "created" by their partner. I'm beginning to go in circles, but I think the two together form a magical paradox, and because of this neither can be completely destroyed unless they are separated from their symbiosis. Points to Julius and crew for figuring out the solution to that hard-ass math problem.