I've never seen anyone bringing a regular bicicle on board of an Italo train.
I can tell you that there is no check-in, and no luggage check... but you might have a hard time for finding a spot for your big luggage (in second class it is often difficult even for a regular luggage) and the train manager will be soon there helping you, and your bag will be surely seen and "checked" in that way.

@jon

@De_Treias @groessenordnung @valhalla Thanks for the help!

For comparison, I've taken packed bicycles on a few Trenitalia frecce, which didn't have much luggage space (even less than - god forbid - SNCF's TGVs) as it's basically only overhead. Which is fine when it's at least 55-60cm deep and slightly slanted, but also a bit stressful that a bicycle might fall.

The experience also varied by train model:
- ETR 500: overhead space was deep enough, and there is a triangle of seats with more space at the end of each carriage 👍
- ETR 700: didn't try overhead as the train was half empty and they were many free seats. Corridor was ok-ish.
- ETR 1000: that train was full so no space left overhead. Corridor between pairs of doors at the connection between carriages was the least bad I found (not sure about safety regulations). I was planning to take an ETR 500, but got rebooked due to delay & missed connection.