Yes. Positions keep the currency they were bought in and are converted into the one you read the account in, so a book spread across New York, London and Frankfurt still produces one balance and one return.
Currency is part of the return rather than a footnote to it. A holding that rose in its own market and fell against your currency shows both.
For tax, purchases and disposals are converted at the official rate of their own trade date rather than at today's rate.
See the multi-currency view