As long as Tsar Michael II confirms that his continuation as monarch is dependent on the upcoming assembly, he has a very good chance of being accepted as at least a titular head. He would be vital in reconciling the conservatives to the new government, and be a key figure for conservatives and moderates to rally around afterwards.
In the short term, it really depends on how much of the army decides to follow him, and whether the nearby soldiers to him and St Petersburg will obey him. If he has no military support, the provisional government will likely ignore him. If he shows up with an army, they'll likely choose to collaborate with him.
In the medium term, much depends on how he acts with the provisional government, particularly with the prime minister. If Michael interferes too much, he may provoke enough political intrigue to inaugur a civil war. If he lies back and allows the PM and provisional government do whatever it wants, he should survive.
In the long term, it all depends on what Russia does next in the war. The people were too exhausted to keep fighting, yet are unlikely to accept any peace Germany would require. Even Lenin had a hard time forcing the Bolsheviks to accept Brest-Litovsk. How any government under Michael handles this will be very decisive. Almost any result is possible. Most likely, the government is forced to accept German demands.
However, if Michael can survive as Tsar for a year, it gives him much legitimacy and makes it far easier to organize the Whites should civil war happen. Most importantly, as Tsar he would be able to force through the concessions the Whites would need to make with other groups - nationalists, liberals, peasants - to unite an anti-Bolshevik front if needed.
So I think lots of things are possible, but it all depends on how things actually play out. Individual decisions are still very important.