I think I have a pretty authoritative response. I have a good friend who is Russian (now a US citizen) and I ran this past her. I told her my take on it was that that, with regards to power, that it was better to have lots of connections rather than lots of money.
“Yes, this is a very common saying back home. My interpretation of it has always been that its not the money but true friendships/relationships that matter (I have never associated it with power, but I suppose it can be). I really dont think it means better watch your back ... It is likely that the author is having such a negative experience with this phrase because there are a lot of bitter Russians out therefrustrated first with shortages, and now with abundance of everything (but lack of money). So they may be thinking he is being sarcastic by using the phrase...”
I want to point out that her English is impeccable; she taught English in Russia, was an interpreter, and is a board certified editor here in the States.
Now, that doesn’t mean you can’t use the phrase any way you like to get your point across, i.e., using it with sarcasm or irony. But I think using it that way without a nod to the original intent weakens the impact of the irony/sarcasm.