Yes, you should be able to highlight text on the client side. Depending on the WebViewer version you are using (HTML5, Silverlight, Flash?) please take a look at the corresponding API Reference (e.g. http://www.pdftron.com/pdfnet/webviewer/demo/html5/doc/index.html, http://www.pdftron.com/silverdox/documentation/Index.html etc...).
Specifically check out classes derived from 'Annotations.TextMarkupAnnotation'. You can also do a programmatic search via DocumentViewer.TextSearchInit (http://www.pdftron.com/pdfnet/webviewer/demo/html5/doc/symbols/CoreControls.DocumentViewer.html#TextSearchInit, DisplaySearchResult etc).
Alternatively, on the server side, you can use 'pdftron.PDF.TextSearch/TextExtractor' (from PDFNet) to search through original PDF document. There is no need to save or re-convert etc. The selection regions / highlights can be sent to the WebViewer (e.g. as an XML request) so that client can show/highlight without any heavy client-side processing. In case you don't like built-in annotations, you can implement a custom annotation (e.g. to show 'hits' etc).
So there are many options. Which one is best depends on your requirements.