Yes, you can write a custom web data connector that Tableau then uses to "scrape" any webpage or webservice (API)
With the Web Data Connector SDK, you can unlock a world of data that's available over the web. In addition to using the dozens of data connectors that are already available in Tableau, you can now create your own web data connector (WDC) that reads data from virtually any site that publishes data in JSON, XML, or HTML.
There are some official connectors, and the community maintains unofficial ones.
So far there is no public OpenFDA connector, but you can write your own.