Linear gradients in SVG without defs

Yes you can indeed have a gradient without needing to have a defs element; you simply put the gradient element anywhere else in the code instead, for example like this:

<svg xmlns="http://www.w3.org/2000/svg"
     xmlns:xlink="http://www.w3.org/1999/xlink">

  <linearGradient id="myLinearGradient1"
                x1="0%" y1="0%"
                x2="0%" y2="100%"
                spreadMethod="pad">
    <stop offset="0%"   stop-color="#00cc00" stop-opacity="1"/>
    <stop offset="100%" stop-color="#006600" stop-opacity="1"/>
  </linearGradient>

  <rect x="0" y="0" width="100" height="100"
     style="fill:url(#myLinearGradient1)" />

</svg>

<defs> is only needed for structuring purposes, the elements in it are not displayed, but since a gradient can only be visible when applied to a shape or another element, you can define it in any place of the document.

But you still have to stick to the correct syntax:

<rect style="fill:url(#myLinearGradient1)" ... />