One issue in the popular screen readers when there is JS is that the virtual buffer (the reader makes a copy of the text on the page, and that is what is read out and what the user interacts with when they use commands to skip around the page) doesn't refresh when JS changes the page... the newest versions of JAWS and Window-Eyes do this better, although they are expensive and it's good to assume people can't always afford to upgrade. Orca screen reader doesn't use a virtual buffer so I'd assume it just reads whatever's after the cursor whether it was put onscreen by JS or not.
So anyway, if you have Firefox and the Web Developer ToolBar, put your JS on the site (if it isn't already) and right-click, look for Web Developer Toolbar in the rightclick menu, choose View Source and then View Generated Source... you'll see the JS-enhanced DOM (instead of the DOM of the HTML you wrote). That's what any JS-using screen reader will be making a virtual buffer of. If there's no text being added, then you're ok either way.
Another side note: many people know that display: none is strangely honoured by most screen readers, even though something positioned offscreen or set to visibility: hidden does not (necessarily). However each reader seems to have its own quirky thing where sometimes, in special cases, something that is display: none does get rendered (read out). For JAWS, one of them was something weird like, an anchor who has a background colour with a display: none span inside, the span gets read out... or something weird like that.
Another thing you can do is get one of the demo versions of one of the more popular readers and take a listen yourself, just to be sure. However if JS isn't adding any text and you just have images with alt="", you should be good.
You can get a 40 minute demo of JAWS from Freedom Scientific (though that company has apparently stated that the they don't like the demo being used by developers... bleh). You can get a demo of Window-Eyes from GWMicro. Those are popular readers for Windows only.
NVDA is a free windows screen reader and it's slowly getting spread around the community, but developers seem to use it more than the average computer user.
If you have a Linux machine with the Gnome Desktop, you likely already have a copy of Orca, the free Gnome reader. You should be able to type "orca" into the terminal to get it started. So far I can only get it to react with Firefox browser though.
There are some other, older readers who are also popular, or were, but may be out of business (I dunno if Dolphin is still in business), but I think you'd be able to catch anything weird going on with just one of the Big 2's demos. They do take some time to get used to.
alt="" is also awesome for Mozilla browser users who have images off for whatever reason, since without alt text, it's as if the image isnt there at all (no space is set aside to show there was an image, no border, no broken-image icon, etc. It's simply Not There : )