They could not do it as easily as the US as the Amphibious capabilities of the Russian Navy are nowhere near as developed as those of the RN and USN, plus they do not have the same level of Strategic Airlift.
They could possibly defeat and occupy iraq as the coalition is doing, however they would still be in the exact same position as the US currently is. Not to mention that i have doubts the russians could sustain such a force for a long period of time supplied only by air and possibly sea.
They can certainly resupply force upto 200,000 in most demanding conditions now. Just look at 90s. they were facing huge chechen , Uzbek,Tajik islamic rebellion in very mountaneous regions. not only that they were the only one who were supplying and training northern allaince in afghanistan (from Kulyab airbase) against very large enemy and that was weaken state of 90s.
Against third world countries u dont need aircraft carriers and against first world Aircraft carrier alone may not work as fighter aircraft from land based fields have higher performance and endurance. It is just different perspective and strategy.
If Russia has to occupy country like Irak it will go through Syrian ports and airspace and is perfectly capable of sustaining the conflict over the years.
First there tactics are different, cost of equipment is cheaper, 30 to 40 years of experiance in fighting anti-terrorist operations. And also knows what kind of government quickly installed to support further actions.
there are joint exercise under CSTO/SCO. So they can also create coalation of willing if there is need of such adventure. Georgia havent faced modern Russian army (precsion strikes with Iskander, Smerch, Masta, Su-27SM etc)and still it melted in less than 3 days. It is bit different than Powell doctorine of overwhelming force.
Strategic airlift is already there with 250 to 500 IL-76, 22 An-124 and countless from Volga Dnpr/AirPolyt/Aeroflot. And there is industrail capacity to make large planes quckly if there is necessity for War strategic airlift
Russia also have large fleet of attack and transport chopers that are much simpler to maintain and use in battlefield condition.
http://www.cbc.ca/canada/story/2007/02/06/big-planes.html
Without big planes, Canada at mercy of Russians: minister