Short answer is no since I don’t think we have a REST end point for doing an HTML export.
One idea might be to add a scheduler job that would execute regularly and perform the export. It would call the export API. The problem is that it won’t work since it’ll be missing things in the context.request.
For fun, example of the Export API in a wiki package:
{{groovy}}
import com.xpn.xwiki.export.html.*
import org.xwiki.model.reference.*
HtmlPackager packager = new HtmlPackager();
packager.setName("TestVMA");
packager.setDescription("Test VMA");
packager.addPageReferences([new DocumentReference("xwiki", "Sandbox", "WebHome")]);
packager.export(xcontext.getContext());
{{/groovy}}
Slightly related: See https://jira.xwiki.org/browse/XWIKI-9123 and the comments there.