The short answer is probably no.
ID, having begun its life as a page layout application, knows nothing about pixels which are units without any physical size. It uses a 1:1 correspondence between pixels and it's native units, points, when you specify pixels as a unit, and points DO have a real physical size, 72/inch.
I suppose you could set up a "custom" point size in the prefs that would give you the desired document size, but I doubt it is worth the effort (but I don't do that kind of screen-only design work). If you set the effective resolution (by scaling) of your images to 72 ppi, you can rely on an unadjusted ID to show you the correct relative sizes.
Peter, it looks like you can only set the point/pica size from 60-80.
Then I guess the answer is definitely no.
But listed size in inches is totally irrelevant if you are working in pixels, so what's the big deal? As I said, if the effective resolution of the elements is 72 ppi, the scale and relative sizes will all be correct. There's a long discussion form a couple months back on viewing at 100% for various devices that you might want to read, too.
I am making a document that will only be displayed digitally.
A lot depends on how the pages will be delivered. If they will be PDF then there's no need to set the page units to pixels because the PDF page magnification is set by your client and can be anything.
If your pages will be displayed in a web browser, you'll have to export them to an image format like jpeg or png. In that case if you export a JPEG or PNG at 72 ppi (or export a PDF and open it in PS at 72ppi) the resulting image size will be your page's pixel dimensions (1440 x 900). Web browsers don't know about inches all that matters is the pixel dimension.