As a matter of fact, the Empire does have the technology to detect, identify, and track firearms all over an entire world, as seen in "A Princess Alone!" (Marvel, 1979). Details are not clear as to how it operates, but the Tagge Weapons Detection System installed on Metalorn enabled Governor Corwyth to do precisely that from a central control room, from which he could "detect unauthorized arms or explosives" anywhere on the planet (and instantly know when a stormtrooper's weapon was "no longer in authorized hands," thanks to the System's pulse beat sensors).
(A somewhat similar surveillance system set up by Commodore the Lord Tion on Ralltiir in "Princess... Warrior" (Dark Horse, 2003) enabled him to eavesdrop instantaneously on the Princess Leia of Alderaan's conversation from across the city, with no more specific selector than "I particularly want to be informed of everything said by Her Highness, Princess Leia.")
As it happens, XaLEv's calculated figure of 5.4 m^3 per soldier would mean that a LH-1740 control core could (in theory) accommodate in excess of 12 million soldiers (
Attack of the Clones Incredible Cross-Sections states that the LH-1740 has some 66 million cubic meters of cargo space, to say nothing of its berthing spaces for 60,000 "trade representatives"). A Rendili StarDrive container train like IFA
Black Ice, with its 100 million cubic meters or so of cargo space, could carry around 19 millions, while a Loronar field secured container vessel (FSCV), which is known from the
Imperial Sourcebook, Second Edition to transport as much as 5.36 billion cubic meters of cargo, could accommodate 993 millions or so.
To give a clearer idea of the vast size of the Empire's merchant navy, consider Mr. Wong's calculations on the Empire's forcible dehydration of Gholondreine- :
Even if the transport fleet was composed of a million ships, each vessel would have had to carry 1.4 trillion tons of water! The density of water is roughly 1 metric ton^3, so each ship would have needed at least 1.4 trillion cubic metres of cargo space. If the transports were cylindrical in shape, they had to be 5 km in diameter and at least 71 km long to have that much internal space! Even if each ship took 1000 round trips, the operation would have required a million-ship fleet of vessels measuring 1 km in diameter and 1.8km long.
Now, then, it would take about 261 Loronar FSCVs to transport 1.4 quintillion tons of water. The
Imperial Sourcebook, Second Edition states that each Sector Group's support fleet has only around 500 ships, of which only 125 are FSCV (125 FSCVs could transport up to 670 billion tons of water). Assuming, then, that FSCVs do not make up the vast bulk of the support fleet's shipping volume, it should only take two support fleets to accomplish the dehydration of an Earth-like world. Now consider that each SectGru is equipped with one support fleet, and consider further that the Galactic Empire has "thousands" of SectGrus. Even if the Imperial State controls only 2,000 SectGrus, it would require less than 1% of the Imperial State's fleet auxiliary to dehydrate an Earth-like planet.
Consider further that a fleet auxiliary is only those ships owned and operated by a state's defense establishment; it does not include ships owned and operated by the state itself, or privately owned and operated shipping lines and tramp freighters. That is to say, the transport of 1.4 trillion tons of water would require substantially less than 1% of the total cargo space of the Empire's merchant marine, which includes such enormous shipping giants as the Tagge Company, Xizor Transportation Systems, Red Star Shipping Lines, the Baron d'Asta's companies, and the Baobab Merchant Fleet.
Simply put, the transport of millions or even billions of soldiers is a trivial task to an economy and defense establishment the size of the Empire's. The only aspect of such an operation that might realistically pose any sort of challenge would be the orderly embarkation and debarkation; more than likely a rapid deployment of such a sizeable force from a single transport is impracticable.
As for the local population's support for the Empire, well... that is another story.