JIRA doesn't track where a request comes from really. If you comment on an issue, you might do it in the JIRA UI, via the Agile stuff, Tempo, via email, over the REST interface, (either gadget or external REST call), import from something and so-on. The source is not tracked because it's not important. The change of data is the important thing, not how you did it. (An analogy a friend used once - I want to drink beer - I don't care if you open a bottle with a corkscrew, a proper bottle opener or it's a screw-top. I get my beer bottle opened)
If you really do need to track sources like that, you'll need to code to include some form of additional tracking.
However, to answer the title of your question, rather than the body, the short answer is "yes". If you create a listener that listens for the right events, then it can push issues through the workflow when certain events arrive.
There is in fact, one already built for you in the JIRA toolkit - the "auto transition listener". It was originally coded to address the case where "we closed an issue, customer comments on it, but because it is closed, we don't report on it". The transition listener listens for "issue commented" and if one happens on a closed issue, then it pushes it through "reopen". (The listener is more flexible though - it can be configured to listen to any event, any point in your workflow and use any transition)
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