Yes, you can display both.
You just need to make sure you are using one of the following tags when displaying your product prices:
The 'sign' will display $ or
The 'word' will display USD or GBP
If that information is not known about a product (because the merchant did not supply that information in their datafeed), the [product.currency mode='sign'] will use the setting you have in your Basic Store Settings in the Factory.