Problem is that as bad the White might have been, they hand not hurt them in the way the soviets did (the aformentioned "food scarcity") I cocnede that it would be seen as a deal witha very proverbial "White Devil" but if they offered a way out of Stalinism I beleive they would take it: As I said before, they took with Hitler.
Just to define things... Problem of hunger in 30-s was 1) overclaimed way later due to political reasons 2) already solved in 1936.
Taking into account that Stalin has managed to "sell" it as local autorities fuck up, there was no problem of really massive social order for "muh, evil commies, let's overthrow them". IRL massive collaboration happened mostly in the territories, got after 1939, Crimea befause of Crimean Tatars and Causasus - mostly Chechens. Last two categories just thought that they have changed sides quickly enough to please the winner and get independence even in the form of German protectorate.
Also, when you say, that Whites didn't hurt people as much as Reds did, you obviously know nothing about neither Russian history, nor exact that period. Nothing personal, just, I - live here, you - are obviously not.
In 1930-s there are still alive people who fought with Whites in Civil war, and people, who remember "White terror" pretty well too. Young generation is grown up on the stories about deeds of "right side" and crimes for the one, who were "wrong ones".
On the other side of problem, White emigrants, who in our history agreed to ally with Hitler, hate the Soviet state itself, the Party and the people. So, if we just assume that things have turned in that fantasy way to give them power, they would be likely to start such a terror that even Mao would be impressed with the scale. So, a new rebellion will be a matter of months. Because it is kind of uncomfortable to live in the state, where rulers see you as "traitors" and sort of "subhumans".
There were plenty of White exiles in Europe and Asia. They had a somewhat legitimate succesor to the Russian Throne. They had more than what was left of the PRC had when they undertook the Long March. Its a situation akin to that of the Japanese COmmies: All te supporters are abroad, its all a matter a briging them in.
Yes, there are plenty of White exiles in Europe. They are disorganized even worse than during Civil war, have completely different vision of political future of Russia and after all, monarchists are a minority. There are somewhat about 3-4 possible "heirs" in that time, who just "fight" with each other, while majority of White emigration are people, who actually supported the fall of monarchy in February 1917. Not bolsheviks have thrown the Nicolas out of the throne - "democrats" have done that.
Also, I must remind you, that NKVD and intel have own people inside White emigration, so, Cremlin knows about everything inside that group earlier than any decision is finally taken.
The figure of the tsar in itself is a powerful thing, so powerful indeed that the SOviets had to purge them thoroughly. And what they can claim is nothing less than the Russian Empire: The Lost Baltic provinces, Eastern poland, Finland, Bessarabia and the dreams of Pan-Slavism all are tied somewhat to the Russian EMpire. And the idea of powerful Empire, that was a Great Power respected and feared, its alluring to a largely desillusioned population. Thats what Hitler did after all.
The figure of the tzar was so powerful, that most White leaders and generals during Civil war were the same people, who supported throwing that "powerful figure" out of the throne in 1917.
And about claims... Soviets have claimed no less than the whole world, united under the red banner of revolution. So, what?
Not to mention he extensive support that the Orthodox Church could give this new Monarch. And the Church was powerful indeed, so powerful that Stalin had to use it during the German Invasion
To be tolerated in Soviet society after the War, Church firstly should have 1) shown unquestionable loyalty to the state 2) provide own help - with propaganda, gathering money for army and etc. After they have done that, Stalin has reached the compromise with the Church - regime doesn't see them until they stay outside of politics.