Multi currency
The app does support selling products in multiple currencies. It can read the currently selected currency and automatically formats the prices accordingly.
The app automatically converts the add-on prices into the customers selected currency.
Shopify Markets
The new Shopify Markets feature from Shopify does allow you to setup multiple markets with different currencies and product pricing.
The app intentionally does not have its own currency rate settings, it will automatically extract the configuration from your store based on the currently selected market.
Add-ons currency
The options add-on prices will always be entered in the base store currency:
When customers currency does not match the store configured currency, the app will auto convert the prices via the currency conversion rate that is configured on your store.
In the example below, the customer is viewing the store with currency set to Japanese Yen:
Add-on products
If you have linked additional products in your options, the app will automatically load the correct price of the linked product in the currently selected store currency.
Draft Orders
Shopify Draft orders now also support multi currency checkout and shopify markets based pricing.
Cart Product
Price currency conversion rounding issues
To prevent rounding issues when using a second product for the add-on, it is recommended to change the price from 0.01 to 1.
For this view the product in your shopify admin:
In the pricing section: 
Change the price to 1.00:
Back in the app, click on the refresh button:
The smallest price add-on will now be 1$, which for most cases should be sufficient.
Currency selector
Shopify supports showing a country and language selector without the need for external apps: Support multiple currencies and languages
Note: most 2.0 themes already have these selectors integrated (e.g the new Dawn theme)
You can also use the Geolocation app offered by Shopify: https://apps.shopify.com/geolocation
Currency conversion apps
3rd party currency conversion apps can use custom ways to auto convert to option prices to other currencies. The app tries to detect use of custom currency conversion app and avoids changing the moneyFormat based on the selected currency.
In our tests with 3rd party currency conversion apps, the outcome was not ideal as the actual price charged at checkout can have differences to the prices shown on the options.
If you are currently using such an app, it is not recommended to enable currency conversion in the Live Product Options app.