If you study French history you'll notice that in the 200 years following the French Revolution they went through 3 monarchies, 2-3 empires, and 5 republics. I'm no exactly sure if following their plan for revolution works - even now in the Fifth Republic (which has existed for about 70 years), things in France aren't always stable.
A referendum on the form of government used is useful in any country where the people are not satisfied with the government, and any country that claims to be democratic should allow for such a referendum if the people demand it.
The problems in Russia - or the US or France, etc - aren't likely to be solved simply by changing the system of government. The problems aren't necessarily because of the system so much as because of the way people are manipulating the system, and the way the voters are allowing that manipulation.
To me, I think if there is strong support for a restoration of the monarchy in any country - be it Russia, France, Romania, etc - then a referendum should happen because that's democracy at play - it shouldn't matter if the person claiming the throne is the deposed monarch, as in Romania, or a descendant of a former monarch, nor should it matter if there is one clear claimant or several. The will of the people is, at least theoretically, what democracy is about.