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>>How many civilians would die in such an invasion?
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>I think 'millions' is safe to say.

I think not, unless your troops would put up some kind of holocaust-like action.

From Wikipedia on Iraq war:

An independent method for estimating the number of Iraq dead is by using national surveys of mortality. A study in The Lancet estimates 654,965 Iraqi deaths (with a range of 392,979 to 942,636) from March 2003 to July 2006, using this methodology <18> <19>. That total number of deaths (civilian and non-civilian) includes all excess deaths due to increased lawlessness, degraded infrastructure, poor healthcare, etc, and includes civilians, military deaths and insurgent deaths.

Wikipedia on Vietnam war casualties(the highest estimate on Vietnamese civilian casualties):

3. Edward Doyle, Samuel Lipsman, et al, Setting the Stage. Boston: Boston Publishing Company, 1981.

U.S. - 57,605. South Vietnamese military - 220,357. Republic of Korea, Australia, New Zealand, and Thailand - not listed. DRV and NLF deaths - 444,000. Combined DRV and RVN civilian deaths -587,000.

Wikipedia on Holocaust(snippets from it's article):

The following estimates provide a range of the number of victims:

An estimated 5 to 6 million Jews,<11> including 3 million Polish Jews
1.8 – 1.9 million Christian Poles and other (non-Jewish) Poles (estimate includes civilians killed as a result of Nazi aggression and occupation but does not include the military casualties of Nazi aggression or the victims of the Soviet occupation of eastern Poland and of deportations to Central Asia and Siberia)<12>
200,000–800,000 Roma & Sinti (Gypsies)
200,000–300,000 people with disabilities
80,000–200,000 Freemasons<13>
100,000 communists
10,000–25,000 homosexual men
2,500–5,000 Jehovah's Witnesses<14>

The following groups of people were also killed by the Nazi regime, but there is little evidence that the Nazis planned to systematically target them for genocide as was the case for the groups above.

3.5–6 million other Slavic civilians
2.5–4 million Soviet POWs
1–1.5 million political dissidents
Additionally, the Ustaša regime, the Nazis' allies in Croatia, conducted its own campaign of mass extermination against the Serbs in the areas which it controlled, resulting in the deaths of 500,000–1.2 million Serbs.

In short, of these three, only holocaust managed to get it's casualty numbers to millions, as was your 'safe' estimate. Hundreds of thousands, quite possibly, but millions, unless your troops are like Nazis..