Even at the height of the Clone Wars, I doubt there were that many Acclamators running around. In fact, I don't think that even if every Star Destroyer was pulled from service just to transport the refugees that there would be close to 23 million ships.
Considering the Industrial capacity displayed by the DS2, I doubt making 23 million Acclamators would be much of a problem, I can't remember the exact numbers, but how many ISD's on average per minute equivilents were the calcs for the rate of construction?
The sudden influx of refugees is going to put a strain on every planet that takes them in, regardless of population already present on the planet, but some worlds will feel the strain harder than others. Start-up colonies, which I assume are some of the newly acquired planets amassed by the Empire, are probably not going to be able to take on that many people right away. Even if they could, the sudden influx of people would overwhelm the population already present, and tensions would mount as people who have probably spent their entire lives in an urban setting look down on the local colonists, and vice versa. Plus, there's the matter of law enforcement as you already mentioned. Refugees usually mean an influx of poverty stricken people who are going to be desperate, and given that large portions of Coruscant are basically huge ghettos, the amount of crime that comes with them is going to be outrageous.
I don't see how a 0.17% increase in population (Assuming earth level populations on average) would be THAT big of an issue, also in Republic/Imperial controlled worlds don't they have replicators and things of that nature?
Not only that, but disease outbreaks are going to be rampant as well. Stuffing thousands of people aboard a ship and then sending them somewhere is a paradise for communicable diseases, which might have been somewhat negated when people were living back on Coruscant. On Coruscant, they could at least somewhat quarantine themselves in their homes. Not so aboard a starship. Even if there were aid stations set up to treat the sick and establish quarantines, being exposed to the sick while waiting in line means that many people won't start showing signs of the disease until after they're packed like sardines. And once they arrive, they're going to be thrown into makeshift barracks, probably packed close together, meaning that if one person is sick, the close confines would make sure everyone gets sick. At least on the planet they're taking refuge on, they can better quarantine the sick.
I'm pretty sure I've already established that the ships are large enough that they don't have to be packed in like sardines, partly for this very reason in fact.
Any evacuation of Coruscant is going to be a giant clusterfuck no matter how you slice it. And the fleet can't exactly rush in every ship available, since if the Federation got away with blowing up one star already, they might do it again. Every ship will be on full alert, ready to mobilize, and I highly doubt any sane Admiral will willingly part with his ships if he catches even the slightest whiff of Starfleet. Coruscant might have gotten away with its massive planetary shield, but what would happen to another target? Like say, Kuat? Or Corellia? Or even Alderaan? What would happen if the Federation used its superweapons against them? They don't have shield generators around every single square kilometer of the planet, so they're in danger of being hit by almost anything.
Again with the Industrial capacity we all know the Empire has, this shouldn't be an issue.
And what if the Federation chose one of those secondary targets first? Or hit them together? No warning, just suddenly BAM! A sudden strike against several highly industrialized worlds. Kuat might get the trilithium torpedo, but Corellia and Alderaan are vulnerable to the Genesis device. And Corellia has five planets, so by the time they realize what's going on, a starship could have launched more genesis torpedoes. One thing I know for sure is that sometimes the threat of violence is enough to terrify, because every single planet in the galaxy will be demanding protection so that they don't become the next target. It would be a huge blow, and no doubt everyone would be panicking.
How exactly are the feddies supposed to suddenly hit anywhere in the SW galaxy at ease now? Simultaneously no less?