I also had the same problem but after some attempts it finally worked. I'm writing here the procedure hoping it will be of some help. I created a simple spiral in inkscape and saved it as svg. Then I opened it in a text editor (e.g. Notepad++) and the entry "style" occured twice in my svg code. First in this chunk:

<linearGradient
   id="linearGradient6172"
   osb:paint="solid">
  <stop
     style="stop-color:#000000;stop-opacity:1;"
     offset="0"
     id="stop6174" />
</linearGradient>

And then here:

<path
   sodipodi:type="spiral"
   style="fill:none;fill-rule:nonzero;opacity:1;fill-opacity:1;stroke:#000000;stroke-opacity:1;stroke-width:35;stroke-miterlimit:4;stroke-dasharray:none;stroke-linecap:round;stroke-linejoin:round"
   id="path4686" />

To make the code work in order to have an editable svg spiral in qgis I completely removed the first "style" entry from the first code chunk:

<linearGradient
   id="linearGradient6172"
   osb:paint="solid">
</linearGradient>

And substitute the second "style" entry in the second code chunk as follows:

<path
   sodipodi:type="spiral"
   fill="param(fill) #000" stroke="param(outline) #FFF" stroke-  width="param(outline-width) 1"
   id="path4686" />

"#000" and "#FFF" are two default colours for the fill and the outline while "1" is the default outline width if not differently specified. After saving these changes you can store the svg in the correct path, the one specified by QGis (depending on the version it can be found in Settings -> Options -> SVG paths). Finally your new svg object will appear among the other default objects and it will be editable.

Hope it can help

I also had the same problem but after some attempts it finally worked.

I created a simple spiral in inkscape and saved it as svg. Then I opened it in a text editor (e.g. Notepad++) and the entry "style" occured twice in my svg code. First in this chunk:

<linearGradient
   id="linearGradient6172"
   osb:paint="solid">
  <stop
     style="stop-color:#000000;stop-opacity:1;"
     offset="0"
     id="stop6174" />
</linearGradient>

And then here:

<path
   sodipodi:type="spiral"
   style="fill:none;fill-rule:nonzero;opacity:1;fill-opacity:1;stroke:#000000;stroke-opacity:1;stroke-width:35;stroke-miterlimit:4;stroke-dasharray:none;stroke-linecap:round;stroke-linejoin:round"
   id="path4686" />

To make the code work in order to have an editable svg spiral in qgis I completely removed the first "style" entry from the first code chunk:

<linearGradient
   id="linearGradient6172"
   osb:paint="solid">
</linearGradient>

And substitute the second "style" entry in the second code chunk as follows:

<path
   sodipodi:type="spiral"
   fill="param(fill) #000" stroke="param(outline) #FFF" stroke-  width="param(outline-width) 1"
   id="path4686" />

"#000" and "#FFF" are two default colours for the fill and the outline while "1" is the default outline width if not differently specified. After saving these changes you can store the svg in the correct path, the one specified by QGis (depending on the version it can be found in Settings -> Options -> SVG paths). Finally your new svg object will appear among the other default objects and it will be editable.