Yes! We support the no-translate feature for Salesforce Live Agent. If you wish for a certain segment of text to be left outside of the translation process, just surround it with (<#text#>) or triple brackets (<<<text>>>).
Please bear in mind that this will not change the position of the text and will exclude it from translation, which may lead to bad translations under some circumstances. We advise the content removed from translation is separated and cannot influence the phrasing in the target language.