How can I tell if a google bot is reading my javascript generated content?
I have an AJAX script that generates some text dynamically on a page... this content does not change by user, but simply by date/time.
I am not sure how I can tell if google sees it.
It doesn't. As far as I know, Google does not yet support JavaScript (or, in fact, any form of dynamic content).
Perform a fetch and render within Google's Webmaster tools. Google will tell you in there. Alternatively, use their page speed test tool. Again, it will tell you if your JS is accessible or not.
The easiest way to know, is to simply copy a chunk of text output within the JS within the browser and perform a search in Google.
I would run it through Google's Webmaster tools site, which has a function to view your page as Googlebot. You may be able to determine it's visibility through there.
https://www.google.com/webmasters/tools/home?hl=en
If you're considering developing a full-blown AJAX website, Google says there's a way of making AJAX applications crawlable.
Short answer: there's an agreement between crawler and server on URIs.
Search engine bots don't have javascript, so they won't see any content that was dynamically added to your page via AJAX, etc. In your browser options, turn off Javascript and reload your website. All that they'll see is the content and the links there.
The solution: on your page, in the plain HTML place a link to a page which shows the rest of your content (the stuff that you would load via AJAX), then have Javascript replace that link with the content. The search engine bots will see the link and follow it, indexing all your content. Just make sure that on these lo-fi pages, you provide links back to the regular page, since that's what Google will link to.
JavaScript generated content is not indexed by search engines. See this question for more info.