Yes

I have been pondering the fine, very tedious, details of ethylene and fruit ripening. Many sites say that when ripening a fruit that responds to ethylene [Several do not.] one can use bananas or apples. Occasionally a site says use ripe bananas. I have yet to see one that says you may use green apples.

[Beyond this it starts to quickly get more complicated. For example many plant tissues produce ethylene when damaged. Some ancients used damaged figs to hasten ripening. Why are damaged apples never mentioned? And then there is the banana story - the fruit distributors add ethylene to cause he banana to ripen [?]. When I put my fruit in a paper bag with the banana does the ethylene come from the banana or from Chiquita ?]

And, do avocado from the store release ethylene when ripening?

I'm not an expert by any means but a quick Google search on "plant production of ethylene" yielded a LOT of good information you might be interested in. Seems that nearly all plants produce ethylene naturally to some degree; domesticated fruit-producing plants much more so due to varietal selection and development over centuries since they typically yielded other characteristics favorable to the grower.