You aren't able to do this in the admin, but you weren't able to do this in the admin in m1 either.
But you are on the right track, but the way you need to do this is in the
default.xml of the theme module. Create a file here:
And include this code:
<block class="Magento\Framework\View\Element\Html\Link\Current" name="gag-my-quote" after="-">
<argument name="label" xsi:type="string">Your Custom Link</argument>
<argument name="path" xsi:type="string">your/custom/link</argument>
It is possible to add in a block into the header that calls a cms block (for future ease of use), it's not that hard to do and can be done in this same file, if you want help setting that up, let me know.