Russia modernizes after the Napoleonic invasion and the Crimean War

  I think it would depend on the nature of the modification.  For instance if its just pushed by one Czar then such an urge might peter out once he's dead.  Given the highly conservative nature of the entire country any big change is likely to meet opposition and for real modification you need better education to produce the technical people for producing roads, bridges, railways etc which will be seen as a threat by the old aristocracy unless the Czar can persuade them to take up that role.  Which could be challenging.  Even then you would only have a relatively small technological elite as I suspect most would prefer to be landholder and the like.  Its also going to be hugely expensive, both directly in terms of structures needed and things like an education programme to provide the skilled manpower and who's going to foot the bill for this?

  Similarly one of the 'lessons' the Russians seem to have taken from 1812 was that there were advantages to being backwards in terms of infrastructure as that made it more difficult for an invader to advance deep into their country.  This is often quoted as a reason why Russia picked a different rail gauge to the rest of the world as it meant that an invader couldn't use rail supply beyond the border until they had changed the gauge.

  I'm not saying its going to be impossible but its going to be tough to get a sustainable modernization programme that doesn't fault without strong support from the imperial family.  The best bet is something along the Japanese model but Japan was a much smaller country and by replacing the shogun with a revived imperial 'rule' it was able to get support for radical change and largely displacing the old military elite whereas to get a broad based social change in Russia would require largely breaking the power of the aristocracy which would be tougher and more dangerous for the monarchy.  Also unlike Japan Russia is a massive empire with multiple communities, even counting the assorted Orthodox Slavs [Russians, Ukrainians & Belarus] as a single group.

  Definitely if Russia had gotten a decent railway system in place between its main centres and Crimea, even without any decent military reform so their forces were properly equipped and trained than a Crimean war type scenario would be vastly more difficult for the allies.  They would very likely still have overwhelming naval superiority but the Russians could basically overwhelm them with numbers and with a decently modernized bureaucracy should be able to keep them better supplied than the allied army relying on sea supply across the Med [and for British forces through Gib and the eastern Atlantic to the British isles].

  Of course a more powerful - militarily and economically - Russia is going to have a hell of a lot of affects depending on when and how rapidly this change starts.  It might be checked to a degree in an advance toward Constantinople but is likely to be a significantly great player in any area where its modern power can reach.  probably not greatly so in the Far East and Central Asia until railways can reach those areas although the more professional military that should be a product of those changes could still have an affect in those regions.  Also of course any intervention in eastern Europe is likely to be more successful.