The term "formal verse" is used to cover form like sonnets, haiku, etc, but a work of literature can have many other types of pattern. For instance the OuLiPo group tried to expand literature by borrowing formal patterns from such other domains as mathematics, logic or chess. Raymond Queneau experimented with many such forms and Perec wrote a 5000 word palindrome "ca ne va pas san dire," and his lipogrammatic novel "La Disparition" lacked the letter 'E'.
With less invasive (but sometimes technically challenging) forms (palindromes, acrostics, etc) it's quite possible for the reader not be be conscious of the form. As Frost suggested, it may be a necessary self-discipline for the writer, a challenge, way to write something that might not otherwise have been written. Forms chosen for the benefit of the writer may not offer the reader much, so should attention be drawn to them? A writer can't fail to reveal that a poem is a sonnet, even if the form contributes little to the effect, but verse (and prose) can have forms that are hard to perceive -
The word is a mist. And then the world is
minute and vast and clear.
The millions of grains are black, white, tan and gray,
mixed with quartz grains, rose and amethyst
With your flair it's not fair that you never got far,
nothing but sour grapes, date rapes, men acting like apes.
Oh Eros, the hot heroes
like you once
a proof of love
I think the pattern of the first would easily be recognised. The 2nd's use of anagrams on alternate lines isn't so obvious though. The choices open to the author are similar to those when allusions are used: signaling the device (using the title, a footnote, indentation, etc) to the reader might prove a distraction, but not doing so risks the author being accused of gaining pleasure from readers not "getting it".