Yes, it is possible to utilize the Transliterate API via iOS using the embedded browser control (whatever they call it these days). Once you've embedded the browser control in your app, you can use the Transliterate API as you would on a webpage. You can find the documentation here:
That said, it should be noted that the Transliterate API has been deprecated for a very long time (i.e., since 2011). Google has recently been cleaning house on their deprecated APIs, shutting down those that have past their sunset dates. I would therefore be extremely reluctant to develop any new app or functionality based on the Transliterate API at this time.
jg