That seems unlikely, but it's a possibility that some Russian analysts have been discussing lately, as discussions between Turkmenistan and its would-be European partners over the pipeline have advanced.
For example, in an article in Nezavisimaya Gazeta and translated in Itar-Tass:
The building of TCP will mean de-facto the recognition of the division of the Caspian Sea into sectors. This is absolutely unacceptable for Russia, and it will have to take action, similar to the operation for the compelling of Georgia to peace. “This time it will have to compel Ashkhabad and Baku to observe international law, probably, with the help of air strikes, if they do not understand any other language. Remembering what NATO did in Yugoslavia, Afghanistan, Iraq and Libya, Russia has no barriers, moral or legal ones, for the use of force in the Caspian Sea,” [Mikheil] Alexandrov [of the Institute of CIS Countries] believes.
And News.Az interviewed Konstantin Simonov, director general of the Russian National Energy Security Fund:
Many people call me a hawk, but I do not deny that this is a matter of prestige of the state – whether Russia is ready to tolerate such an outright move of disrespect. If Russia’s allows to treat itself in a way Tajikistan did a couple of days ago trying the crew of the Russian aircraft, the Trans-Caspian gas pipeline will become possible.
But what we see today is that Turkmenistan, despite the support from Washington and Brussels, is not ready to risk yet. I am very doubtful that Russia will tolerate it. Moreover, the reaction can be very hard up to some sort of military conflict in the Caspian Sea.
Is Turkmenistan ready for this? I have great doubts in this regard.
In mid-October, Russian President Dmitry Medvedev held a meeting with permanent members of the Security Council on cooperation between the EU and the problems of Trans-Caspian pipeline. The Russian leader stressed that Russia must formulate its position and "bring it to the attention of our partners in the Caspian Sea should they make certain decisions."
Russia, obviously, has an interest in stopping gas from Turkmenistan from going to Europe, as it would reduce Gazprom's market share in Europe. Given that this could substantially reduce Russia's income from natural gas, which has been the main driver of its boom over the last decade, it would seem to be pretty solidly in the national interest to keep such a pipeline from materializing. But does that mean they would resort to air strikes against Azerbaijan and Turkmenistan, as Alexandrov suggests?
To bomb another country simply for building a pipeline would be beyond the pale. So (and this will start to be wildly speculative) Russia would need a pretext to intervene, and it's hard to imagine an appropriate one arising in that region.
In any case, the recent bellicose rhetoric from Kremlin-connected commentators is almost certainly nothing more than saber-rattling intended to spook potential partners and investors. But if they don't get spooked and the pipeline looks like it's going forward, things could get interesting.