No, at least one poet used sentence fragments in large scale in some of his poems nearly a century before Walt Whitman.
This was Christopher Smart, who wrote unconventional poetry in the 18th century.
His most famous poem is probably For I will consider my cat Jeoffry, which consists almost entirely of "for" phrases, and is vaguely reminiscent of some of Whitman's poetry. Here are two excerpts:
For having done duty and received blessing he begins to consider himself.
For this he performs in ten degrees.
For first he looks upon his forepaws to see if they are clean.
For secondly he kicks up behind to clear away there.
For thirdly he works it upon stretch with the forepaws extended.
For fourthly he sharpens his paws by wood.
For fifthly he washes himself.
For sixthly he rolls upon wash.
For seventhly he fleas himself, that he may not be interrupted upon the beat.
For eighthly he rubs himself against a post.
For ninthly he looks up for his instructions.
For tenthly he goes in quest of food.
For he is of the tribe of Tiger.
For the Cherub Cat is a term of the Angel Tiger.
For he has the subtlety and hissing of a serpent, which in goodness he suppresses.
For he will not do destruction, if he is well-fed, neither will he spit without provocation.
For he purrs in thankfulness, when God tells him he's a good Cat.
For he is an instrument for the children to learn benevolence upon.
For every house is incomplete without him and a blessing is lacking in the spirit.
For the Lord commanded Moses concerning the cats at the departure of the Children of Israel from Egypt.
For every family had one cat at least in the bag.
He also wrote rhymed poetry with sentence fragments; Here is an excerpt from A Song to David; this part of the poem is mainly a series of adjectives and noun phrases:
Great, valiant, pious, good, and clean,
Sublime, contemplative, serene,
Strong, constant, pleasant, wise!
Bright effluence of exceeding grace;
Best man!—the swiftness and the race,
The peril, and the prize!
Great—from the lustre of his crown,
From Samuel's horn and God's renown,
Which is the people's voice;
For all the host, from rear to van,
Applauded and embrac'd the man—
The man of God's own choice.
Valiant—the word and up he rose—
The fight—he triumph'd o'er the foes,
Whom God's just laws abhor;
And arm'd in gallant faith he took
Against the boaster, from the brook,
The weapons of the war.
Pious—magnificent and grand;
'Twas he the famous temple plan'd:
(The seraph in his soul).
Foremost to give his Lord his dues,
Foremost to bless the welcome news,
And foremost to condole.
These two poems, however, seem not to have been widely appreciated until well after his death. Jubilate Agno, which "My Cat Jeoffry" is an excerpt from, was not published until 1939.