While I appreciate the points made by the other answers, I don't find them satisfactory enough (maybe only a comment by a designer would be enough), so allow me to post my interpretation.
The Hurl Through Hell ability is somewhat similar to the 4th level Banishment spell:
You attempt to send one creature that you can see within range to another place of existence. The target must succeed on a Charisma saving throw or be banished.
If the target is native to the plane of existence you're on, you banish the target to a harmless Demiplane. While there, the target is Incapacitated. The target remains there until the spell ends, at which point the target reappears in the space it left or in the nearest unoccupied space if that space is occupied.
There are of course differences: Banishment is a spell, requires a failed save, concentration and has other effects. But here the ramifications are clear: the affected creature is incapacitated and cannot do anything (interestingly, it also loses concentration, which would be another side question for Hurl Through Hell).
With the principle for 5e that spells and abilities do exactly what they do and nothing else, it can be deduced that something that is explicitly written (being incapacitated) in one spell, but not in a similar ability, is not applicable in the latter.
By RAW, the affected creature can take an action (keeping it's initiative) while gone.
An argument could be made that the designer's intention was the opposite and the clarification made in Banishment was forgotten for Hurl Through Hell, especially since it is a rather niche ability. More so, Banishment explicitly sends you to a harmless demiplane, while Hurl Through Hell sends you to a dangerous lower plane. It would make sense for the affected creature to have it's own abilities hindered in some way. But unless we get Crawford or someone else to pitch in, we cannot rely on that.
As for the ramifications, still according to RAW:
The affected creature can ready an action, as long as the trigger is a perceivable event (coming back is certainly noticeable). If it readies a spell, it will need to roll a CON save to keep it's concentration when it takes the 10d10 psychic damage.
The creature is on another plane and can use spells to change plane as always. But if it is not there already, it will come back to it's original position at the end of the Warlock's next turn. It takes the 10d10 psychic damage.
The creature does not see the original battlefield (unless it uses some sort of divination magic) and cannot predict exactly what the characters will have done before it's return.
Of course all of this is subject to the DM's ruling. He could certainly decide that the affected creature, while gone, is in no shape to do any kind of actions (giving more weight to the 'Hurtles' word in the description, which means: move or cause to move at a great speed, typically in a wildly uncontrolled manner). Likewise, the DM could decide that the creature not only can escape it's hell, but by doing so will prevent some, if not all, of the psychic damage. A save would be appropriate.