I think the problem here is not so much the issue in and of itself, but the numbers. With the German authorities deposed and the Allied (especially Soviet) authorities not really being trusted by the population, we're facing a potentially huge number of unreported / undocumented cases, and estimates about them.
Those are hard (impossible) to reliably source. All you can source is the people making those estimates.
Naimark actually says the very same thing:
"It is highly improbable that historians will ever know how many [...] were raped."
(Norman M. Naimark: The Russians in Germany: A History of the Soviet Zone of Occupation, 1945–1949. The Belknap Press of Harvard University Press, Cambridge (Massachusetts) 1995, p. 132 f.)
Two million is about the upper limit I have come across, actually an estimate for the Russian sector alone up until 1947.
(Christine Eifler, Krieg - Gewalt - Geschlecht, in: Krieg, Geschlecht, Traumatisierung. Publisher Medica mondiale e.V. / Marlies W. Fröse / Ina Volpp-Teuscher. Frankfurt a.M. 1999, 87-95, 91.)
That number is critizised, as "definitely overstated" for example by Miriam Gebhardt. Starting with 8,600 children born by rape victims (in the whole of Germany), she estimates about 860,000 cases, about half of them by Russian soldiers.
(Miriam Gebhardt: Als die Soldaten kamen. Die Vergewaltigung deutscher Frauen am Ende des Zweiten Weltkriegs. DVA, München 2015, p. 32 f.)
Cornelius Ryan, in his book "The Last Battle" (Collins, London 1966), states that doctors he talked to estimated between 20,000 and 100,000 cases of rape. (Though time range and area of that estimate is unclear from the secondary source I have -- and those are doctors, not historians or policemen or whatever, and from the Allied side of what rapidly turned into the frontline of the new cold war.)
So, even without making any estimates, and using Gebhart's number of children born to victims, we have almost ten thousand known cases.
The various estimates then go forth adding various factors of
- women who did not make it known their child was the result of rape,
- women who died during or after the ordeal, from injury or suicide,
- women who didn't conceive or miscarried (conception is not exactly the purpose of a rape in the first place)
to arrive at their numbers.
On the other hand, we have the Russian counter-claims that the practice was "not widespread" because there was an order against it... leaving aside the question of how well that order was actually enforced by the local officers, "not widespread" (if that is indeed the Russian wording) is somewhat of a weasel word (no offense intended).
Karl Bahm for example, historian at the University of Wisconsin, states that "of course not everybody behaved this way, but a not too small minority did". (Karl Bahm: Berlin 1945. Die letzte Schlacht des Dritten Reichs. Klagenfurt 2002, p. 159 f.)
In an army of (literally) millions, how much of a "not too small minority" or "not widespread" habit does it take?
So, to answer your question:
...did rape by the Soviet troops during the occupation of Germany occur in the huge numbers described above?
In exactly the numbers described? We cannot say. The two million number is on the high side of estimates.
In significant numbers, big enough to be called "huge"? Yes.
For the sake of political correctness:
There are various orders by the German high command that, if not actually encouraging sexual violence by Wehrmacht soldiers, did discourage persecution and punishment, at least in the east. (Order of the OKW 1940-07-05, Kriegsgerichtsbarkeitserlass 1941-05-13)
Nevertheless, there are 5,349 convictions of German soldiers for "acts of indecency" on file.
(Birgit Beck: Wehrmacht und sexuelle Gewalt. Sexualverbrechen vor deutschen Militärgerichten 1939–1945. Paderborn 2004, p. 326 f.)
How many actual cases that amounts to is anybody's guess.
One does not excuse the other.
All sources lifted from the German Wikipedia articles on the subject, i.e. The Battle of Berlin # Aftermath and Sexual Violence in WWII, and paraphrased into English by myself.