Does a triggered ability that triggers at the beginning of upkeep trigger even if the permanent that has it entered the battlefield during upkeep?

Triggered abilities watch for their trigger condition continuously. A 'at the beginning of upkeep' ability uses a triggered ability that looks for the beginning-of-upkeep event, which is represented by the game creating a triggered-ability trigger when the Upkeep Step starts (CR 502.1). However, if a permanent enters the battlefield during the upkeep step itself — say, because another triggered ability or a spell put it there — the beginning-of-upkeep event has already passed, so the newly arrived permanent misses that event.

CR 603.2 states that a triggered ability triggers whenever its trigger event occurs, and CR 603.3 clarifies that a triggered ability that would trigger at the beginning of a step or phase only triggers if it is on the battlefield (or in the appropriate zone) at the moment that step or phase begins. If the permanent wasn't present when the Upkeep Step began, it cannot 'look back in time' to catch the already-occurred event.

So the real answer is: No, not if it entered during upkeep. The beginning-of-upkeep event is a single moment at the start of the step. A permanent that enters after that moment has already passed misses the trigger entirely and must wait until the next turn's upkeep.

Example: You control no permanents at the start of your upkeep. Your opponent's Aetherflux Reservoir trigger resolves and gives you life, and as a result some effect puts Ajani's Welcome (which triggers at the beginning of your upkeep) onto the battlefield. Ajani's Welcome does not trigger this upkeep because the beginning-of-upkeep event already occurred before it was on the battlefield. It will trigger at the beginning of your next upkeep.

In summary: a 'beginning of upkeep' triggered ability only triggers if the permanent was already on the battlefield when the upkeep step started (CR 603.2, 603.3). Entering the battlefield partway through upkeep is too late to catch that trigger event.