No.
A carnet is not about citizens - it's about vehicles.
And it's not about them returning to country of residence - just leaving certain the countries that require carnets or advance payment of potential Customs Duty.

As Mark said it is effectivly a "returnable deposit' equivalent to the possible liability should the vehicle not properly exit a country within the permitted time. In such circumstances that country is entitled to assume the vehicle has been imported and would expect to receive Import Duty.

That potential for Import Duty is what the carnet guarantees to the Customs of the country you are entering should the vehicle not exit properly.
The issuer of the carnet would require to hold a deposit from you to cover his potential pay-out. (Would you trust a stranger?)
The deposit you leave with the Carnet Issuer will be fully returned to you when you return the Carnet with all the pages whole or properly completed and stamped in and out of countries requiring it.

Sure they charge a Fee for doing this - but think of the paperwork, hassel and risk it saves from carrying equivalent amounts of cash in each local currency to deposit on entry and later collect on exit, for each country on your journey that requires them.

Back to your other question - as your start/finish is in UK, I assume you have UK citizenship and a UK registered bike as well,
You can very easily RTW with only one Visa and no Carnet at all. You only need buy additional insurance to your normal UK/EU insurace in 2 countries.

It's so easy even actors and OAPs can do it!

From UK - ferry/tunnel to France, ride through EU to Latvia - ride across Russia to Vladivostock (insurance & visa needed) - ship to USA or Canada (insurance needed) - ride to east coast and ship back to EU.

Russian insurance should be no more than about GBP 10 per month. Visas costs vary depending on type, duration etc.

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