I used to do this exact thing! I had JIRA send an email for every new task assigned to me but set the email address to me OmniFocus email. It meant that everything landed in my OmniFocus setup. I simply knew (based on the formatting of the task in OF) that when I worked on those JIRA tasks, I had to update the online system.
But to be honest, given the same setup today I wouldn’t do this. Currently, I have a bunch of team projects and tasks in a Discourse instance for ProCourse. I could technically get these into OmniFocus but it’s kind of nice to keep them separate and just plan on working two different systems from two different times/mindsets.
So my question here is why? What do you feel you gain by consolidating? Is there a device constraint causing you to look for this or is it just because you want to? “Want to” gets in my way a lot.