Divine Power says a bit about "folk" religious practices on pp 39 and 143. I think that the default orientation of 4e is that the gods are active in the world, and that prayers to them matter.
Obviously in Dark Sun, or a Conan-esque game, it would be different; but then in such a game I don't think the action declaration in the OP would come up.
Thanks for the specific page citations. I feel such references are useful.
I think of the Forgotten Realms as a fairly active and interventionist divine cosmology for D&D with a lot of god manifestations.
A number of Forgotten Realms sources discuss how people in that setting will commonly pray to different gods for blessings or warding off of evil all the time depending on the specific thing they are doing, so Chauntea the agriculture goddess when farming, but Auril when it is cold out or Umberlee when sailing. I don't remember a lot of discussion of deific answers though. The 2e god books would have deity specific lists of things they would do to express favor or disfavor, but these were still usually fairly limited manifestations and seem to come from capricious gods expressing favor or disfavor, not in response to prayers.
Faiths & Avatars for instance on page 21 explaining the god entries says for manifestations other than avatars:
Other Manifestations
This section discusses other manifestations of a power aside from its avatar. These manifestations are much more commonly encountered than the actual avatar of a deity. They often convey benefits to the faithful or indicate favor, direction, danger, agreement, or disagreement by the deity. Sometimes they are merely used to comfort and assure their worshipers that they are aware of a situation or appreciate their followers’ devotion.
The first god entry, Akadi, says this on page 24:
Akadi has sent manifestations to the Realms more frequently than she has sent an avatar, but even these appearances are extremely rare compared to the frequency with which other powers manifest. The Lady of Air has appeared in the form of almost any normal flying creature, and her voice has been heard as a gentle whisper upon the breeze. She frequently sends an aerial servant to deliver private messages (or demands) to those she deems worthy or useful.
A rising breeze or a change in the wind is usually seen as a sign of her favor.
Eldath, who I earlier was mistakenly remembering as a goddess of healing springs is a good goddess of peace, springs, pools, waterfalls, and druid groves but not specifically healing says on page 57:
Eldath appears most frequently as a whispering wind that brings a message and revives plants that it touches to the blooming height of health or a green glowing aura that has all the healing powers of the goddess, can speak aloud and in the minds of those within 120 feet, and can telekinese nonliving items within its confines. Eldath also acts or shows her favor through the appearance or actions of bears, raccoons, brownies, dryads, sylphs, nereids, feystags, sprites, stags, talking owls, unicorns, and other woodland creatures, common meadow and woodland flowers such as daisies, water plants such as water lilies and lotuses, and aquamarines, clear quartz, blue topazes, sapphires, and other stones in watery hues.
Her avatar neutralizes poison by touch and is a 30th level mystic which is a variant full spellcasting priest class, so that glowing aura manifestation can do some serious healing.
Lathander is similarly over the top.
page 91:
Lathander manifests his power as an intense rosy radiance surrounding the bodies of those he favors. Lathander’s radiance also appears around objects to indicate special qualities about them and at confusing or dangerous junctures to indicate a safe or preferred path. This radiance causes those people it surrounds to be healed of all wounds, purged of any diseases, poisons, foreign objects, afflictions (including lycanthropy, feeblemindedness, insanity, and blindness), magical or psionic compulsions, fear, and curses. The radiance also telekineses people for short distances to get them out of harm’s way. (They may be lifted out of a trap or out of the reach of enemies.)
The faithful of Lathander who are surrounded by the radiance also receive a brief message of some type from Lathander to guide them. Others may receive similar impressions if Lathander desires. If the radiance appears around a corpse of one of the faith, resurrection survival is automatically successful while the radiance is present.
Finally, Lathander sometimes uses robins, sunpeacocks (animals he favors for their plumage), sunpeacock feathers, butterflies, and aster blossoms as signs of his presence or favor.