In Designer if you import an SVG with images relative to the SVG file and referenced correctly with the image href it doesn't show the image when imported.
Here is an example of the SVG code which doesn't import correctly in Designer ( but works in Safari, Preview and Illustrator ).
<g id="Background">
<image width="3658" height="2295" xlink:href="links/themeTime_01.jpg"></image>
</g>
There is also no option to export an SVG without embedding the image in the SVG itself. For our studio this workflow is really important and a major barrier to switching over to Designer full-time.
In Illustrator you can export SVGs with images included as relative links. Which produced SVG code similar to above.
See the image location options here: