Definitely passing webpart values to XSLT is possible for all classes which inherit from DataFormWebPart, and can be easily done through ParameterBinding:
<ParameterBinding Name="WPPropertyBinding" Location="WPProperty(Title)" />
Use your custom property name instead of Title
.
If you're using a standard SummaryLinkWebPart and you need only to fix XSL transformation, then all you have to do to achieve this, is to add the parameter binding string shown above to ParameterBindings property of SummaryLinkWebPart.
Then, in XSLT, reference this parameter using following xsl code:
<xsl:param name="WPPropertyBinding" />
From this point, you will be able to use the parameter in XPath queries, for example:
<xsl:value-of select="$WPPropertyBinding" />
Read more about ParameterBindings on Stefan Stanev's blog, he has a really comprehensive article about it: