Does a permanent entering the battlefield trigger 'enter the battlefield' abilities if it was put there by a replacement effect?

When a replacement effect modifies how or where a permanent enters the battlefield, it changes the circumstances of entry — but the permanent still enters the battlefield. Any triggered ability that watches for a permanent entering the battlefield will still trigger. CR 614.1c confirms that replacement effects modify an event; they do not prevent the event from occurring entirely.

Triggered abilities that use the phrase 'enters the battlefield' or 'when ~ enters' watch for the event of a permanent arriving in the battlefield zone (CR 603.2). As long as the permanent ends up on the battlefield, those triggers will fire, regardless of whether a replacement effect shaped how it got there.

It's important to distinguish replacement effects from prevention effects or effects that redirect a permanent to a different zone entirely. If a replacement effect sends the object to a different zone (e.g., exile instead of the battlefield), then the permanent never enters the battlefield at all, and no 'enters the battlefield' triggers occur — but that is because the permanent did not reach the battlefield, not because of the replacement effect per se.

Concrete example: Your opponent controls a Leyline of the Void, which replaces permanents going to the graveyard with exile instead. This is irrelevant to entering the battlefield. Meanwhile, you cast Elesh Norn, Grand Cenobite. A replacement effect from Torpor Orb suppresses triggered abilities — but absent such suppression, if Elesh Norn enters the battlefield (even modified by some replacement effect like entering tapped), any 'enters the battlefield' trigger on another card that watches for creatures entering will still fire normally.

So the rule is straightforward: replacement effects that modify entry do not prevent 'enters the battlefield' triggers. Only if the permanent is redirected away from the battlefield entirely (never actually entering it) would those triggers fail to occur. (CR 614.1, 603.2, 603.6d)