Does usage of Counterparty's smart token system burn any XCP?
I assume you are referring to smart contracts? Then yes. Xcp is used as gas for the contract execution
Aren't Counterparty's smart tokens completely distinct from its smart contracts?
Yes, the tokens are separate. The "smart" terminology is a bit confusing. You can just call tokens, tokens. That way there will not be confusion with the smart contracts, which, as Matt mentioned, will use XCP as gas.
Tokens are .5 XCP to create. The XCP is burned.