Will state triggers cause a draw if their condition is always true?
In general, a state-triggered will trigger repeatedly and draw the game if its trigger condition continues to be true, but the situation you describe does not meet that prerequisite, so the game will not be a draw.

Once the three relevant permanents are on the battlefield, the next time Hidden Predators triggers, it will stop being an enchantment again, and the game will just go on as usual.

Lets say we have the state where Hidden Predators is already a creature, your opponent controls a creature with power 4, and you cast Enchanted Evening. The game plays out like this:


Immediately after Enchanted Evening resolves, two relevant continuous effects apply from Hidden Predators and Enchanted Evening respectively:


Hidden Predators is a 4/4 Beast Creature.
[Hidden Predators] is an enchantment in addition to its other types.


They are applied in timestamp order, so the result is that Hidden Predators is a 4/4 Beast Enchantment Creature.
Now, all of the conditions are met, so Hidden Predators' triggered ability triggers again.
Hidden Predators' triggered ability resolves, and we get an additional relevant continuous effect:


Hidden Predators is a 4/4 Beast Creature.
[Hidden Predators] is an enchantment in addition to its other types.
Hidden Predators is a 4/4 Beast Creature.


Again, these effects are applied in timestamp order, so Hidden Predators is once again just a 4/4 Beast Creature.


After that, Hidden Predators is once again not an Enchantment, so the ability does not trigger.

The rule that governs this interaction is 613.6:


  
  613.6. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an earlier timestamp is applied before an effect with a later timestamp.
  
  
  613.6a A continuous effect generated by a static ability has the same timestamp as the object the static ability is on, or the timestamp of the effect that created the ability, whichever is later.
  613.6b A continuous effect generated by the resolution of a spell or ability receives a timestamp at the time it’s created.
  
  




In a different situation, with different state-triggered abilities, those abilities can cause a draw. For example, as diego mentions, if you control a Darksteel Reactor and your opponent controls a Platinum Angel, then the ability just triggers forever in a loop that can't be stopped unless a player can remove one of those permanents at instant speed.