Hi Kevin,
I don't think anything would change for you unless you applied for Russian Citizenship and went with a dual status. Otherwise you are still traveling on a US passport and have to deal with all the issues.
Personally, by the time you are dealing with this it may not be an issue. It gets easier and easier to go to Russia. When I think back to my first trip in 1996 and what I went through in Customs and compare it to now it was amazing. There were no agencies to help with the visas, even the Russian Embassy would not give you the time of day. You had to show your money, your bags were searched you spent 5-10 minutes with the passport control. Now the visa is more like a tax. You just spend a minute with the agent, pull your bag right through the green line and wade through the horde of cab drivers looking for you money. Give it a few years and it will be like going to western Europe.