Is there an API to find Warhammer 40K model pictures by name?
I sincerely doubt there is, at least not officially.  I've been playing Games Workshop games for the past 15 years, and their protection of intellectual property has gotten pretty severe in the past couple of years.  Just do a Google search for "Games Workshop sues" and see all the fun that auto-complete brings up.  

From their Legal Page, Bandwidth Theft and Mirroring Resources section:


  We do not tolerate deep linking to the pictures, images, PDFs or other downloads on our website. Such activity is bandwidth theft. Also, do not mirror the resources that we have on our websites. So, if you want other people to see the materials that we have produced, please use a simple HTML link to the relevant web page.


And from the Online Auctions:


  Do not use our trademarks in relation to products that are not owned by or originate from Games Workshop (see Making Terrain above).


Now, I am not a lawyer, but between Privateer Press, Chapterhouse Studios, the TalkFantasyFootball forums, etc., etc., I would be very careful in what you do.