Yeah, the test mode of Twine 2 doesn't show images from relative urls in test mode, which means you'll have to publish to file to see your images. The online version is the same way -- you can't actually have relative-sourced images online, so, yeah. Images you get from an external source with a complete url are fine in either version.
Also, there are other compilers you can use like Tweego and Twine 1, but they actually don't use Twine 2's weird stripped down test mode at all, so your only option is to compile.
Compiling to test your images really isn't that big of a deal. If that's your only concern, that strikes me as an odd one. The test mode in Twine 2 is weird because it does all the work of building and compiling your story, but it keeps it in memory rather than saving it. That's pretty much the only difference.