I'm pretty confident that the answer is yes for each country.
France (>.95) This alliance definitely wins. Using casualties as an indirect measure of military strength, France is third most (after Germany and Russia). But this is a total counter-factual because there is essentially no historically plausible path to WWI that leads to France and Germany on the same side.
Historically, I believe the last alliance between those states before WWI was the War of Austrian Succession (and Prussia was not unified into Germany at that time).
Russia (>.75) Second most casualties, but with the benefit of hindsight, there's strong reason to think this overstates Russian military power - although Russia defeated Napoleon and would go on to defeat Hitler with minimal assistance. Still, even assuming that Russia is equivalent in military power to the second raters like Ottoman Empire and Italy (a very questionable assumption), the removal of the Eastern Front probably adds enough German troops to the Western Front to overwhelm France.
UK (>.65) Fourth most casualties. Fought on the same front as France, so removal of those troops increases leverage on the outcome of the France-Germany fight. As you may know, the French army barely made it through the war, so lack of other forces to absorb casualties seems plausible for swinging the outcome.
The standard view of Mutually Assured Distruction (MAD) is something like:
Occasionally people will reply with an argument like:
This is an anthropic argument, an attempt to handle the bias that comes from a link between outcomes and the number of people who can observe them. Imagine we were trying to figure out whether flipping "heads" was more likely than flipping "tails", but there was a coin demon that killed everyone if "tails" came up. Either we would see "heads" flipped, or we would see nothing at all. We're not able to sample from the "tails: everyone-dies" worlds. Even if the demon responds to tails by killing everyone only 40% of the time, we're still going to over-sample the happy-heads outcome.
Applying the anthropic principle here, however, requires that a failure of MAD really would have killed everyone. While it would have killed billions, and made major parts of the world uninhabitable, still many people would have survived. [1] How much would we have rebuilt? What would be the population now? If the cold war had gone hot and the US and USSR had fallen into wiping each other out, what would 2013 be like? Roughly, we're oversampling the no-nukes outcome by the ratio of our current population to the population there would have been in a yes-nukes outcome, and the less lopsided that ratio is the more evidence that MAD did work after all.
[1] For this wikipedia cites: The global health effects of nuclear war (1982), Long-term worldwide effects of multiple nuclear-weapons detonations (1975). Some looking online also turns up an Accelerating Future blog post. I haven't read them thoroughly, and I don't know much about the research here.
I also posted this on my blog