Does Sitecore SXA out-of-the-box search functionality have option to include external (non-sitecore hosted) sites to include in search result?
You can read details on SXA search configuration in the online documentation here: https://doc.sitecore.net/sitecore_experience_accelerator/setting_up_and_configuring/setting_up/sxa_search
The relevant piece for your question is:
SXA supports both Lucene and Solr search engines. The search engines are used for searching in the content databases, as well as for searching in a number of operational databases that Sitecore uses for collecting analytics data, test data, and so on.
SXA Search is index-based, therefore it will only crawl what is in the indexes.