If such a thing did occur then the big parties would probably be the Social Revolutionaries [largely based in the country] Mensheviks [urban workers] and the more centralist Kadets. The Bolsheviks would probably pick up some votes but less than OTL although they might be concentrated in the military.
What sort of policies would this government follow? Probably seeking a negotiated end to the war and land reform. The former would cause problems for the allies, especially once they rejected any such peace - since it would still leave Germany with substantial gains even if it was prepared to give up all its western conquests - but they may not be able to do much. The latter would be an horror to the assorted conservative elements so you are likely to end up with some right wing 'White' rebellions but, unless they gain external support they are likely to be quickly repressed. [Possible questions here about the Czech Legion, which will want to fight but its likely to be allowed to travel east to Vladivostok and also Japan as to whether would it seek to 'support' a threatened imperial dynasty and hence intervene in the east?]
The other issue is would Germany accept say peace on the current front lines or would they insist on further gains? They would be sensible to do the former but we are talking about imperial Germany which while not as insane as its later Nazi version did have fairly frequent diversions from reality.
If so they would be able to get more troops from the east and a bit sooner - as their seeking to occupy less land - but probably can't attack on any large scale much earlier because an offensive in mid-winter would be very difficult. They probably have a bit more success than OTL but the logistics are against them, especially where their advancing across territory they devastated in their retreat ~14 months ago. As such 1918 is bloody but the CPs still go down. Which would have some impacts on the following peace as there's at least a possibility that Russia has some influence on the peace treaty. Even if not formally present it exists as a non-pariah state and if it avoids the civil war and following oppression is definitely going to be considered a player in the affairs of eastern Europe at least.
How Russia fails is the big issue. Its very difficult with such a vast country and little/no real experience to build a stable democratic state and it will be threatened from both extremes as Lenin and his gangsters won't want to give up their hopes of control while there will be a lot of unhappy army officers, landowners, clerics and special interest groups like the Cossack's. Also how does the government respond to demands for autonomy if not outright independent from assorted national groups.
One issue is it might be better for Russia - but probably worse for the western powers - if the election occurred before the
Kerensky_offensive starts at the beginning of July. This would leave Russia in a better position to stabilize possibly although potentially a right wing coup against the government might be more dangerous. The army is somewhat less undermined and Lenin doesn't have the failure of the offensive and resultant unrest to boost his position.
en.wikipedia.org