Absolutely it would.
611.3c Continuous effects that modify characteristics of permanents do so simultaneously with the permanent entering the battlefield. They don’t wait until the permanent is on the battlefield and then change it. Because such effects apply as the permanent enters the battlefield, they are applied before determining whether the permanent will cause an ability to trigger when it enters the battlefield.
Example: A permanent with the static ability “All white creatures get +1/+1” is on the battlefield. A creature spell that would normally create a 1/1 white creature instead creates a 2/2 white creature. The creature doesn’t enter the battlefield as 1/1 and then change to 2/2.
Threefold Thunderhulk will enter with three +1/+1 counters on it, and also get the +1/+1 from Anthem of Champions, meaning that it enters as a 4/4 creature, and so when its enters trigger resolves you will get 4 token creatures.
Even if this weren’t the case (e.g. if the anthem effect were applied as some kind of state-based action) then it would be fine – Thunderhulk is already on the battlefield once the trigger resolves, so it will definitely have 4 power at that point. However, it does mean that Thunderhulk will trigger, for example, Garruk’s Uprising, which says
Whenever a creature you control with power 4 or greater enters, draw a card.
because its power is equal to 4 as it enters which wouldn’t be the case if rule 611.3c worked differently.
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