No.
Here are some quotes compiled by Lightningstar that support the Jay x Stick shipping!
Jaypaw ran his paw over it [the stick]. The exposed wood felt sleek beneath his pad.
Page 61
Why wasn't she [Leafpool] more interested in the stick? They had never come across anything like this before. Reluctantly, Jaypaw slid his paws from the branch. His pads felt warm where he had been touching it.
Page 62
He [Jaypaw} paused. What about the stick? He couldn't just leave it where it was. It might get washed away. He... began to role the stick up the waterline with his paws.
"We can't carry that home as well," Leafpool meowed, returning to his side...
"But we can leave it somewhere safe," [Jaypaw said].
I want to come back and look at it again.
Page 62-63
A spark of anxiety flickered in his chest at the thought of losing the stick to the lake.
"Come on." Leafpool sounded impatient.
Jaypaw darted back to pick up the leaves he had dropped and followed her into the trees. His paws felt heavy and unease flickered in his chest. Leaving the stick felt wrong. He wanted to understand why.
I'll be back, he promised.
Page 63
He hadn't realized that they had come this far around the lake.
His paws tingled with excitement.
The stick.
...He could smell the stick now, its strange scent calling to him like a kit mewling for its mother. He hurried to where he had left it tucked behind the tree root and dragged it out onto the shore. He wanted to run his paws over it again, feel the scars in its smooth surface. His pads felt warm as they stroked it, his heart suddenly as full as a well-fed belly.
Page 154
"Why are you so interested in it [the stick]?" Leafpool was puzzled.
"It feels important!" He rested both paws on the wood, as smooth as spider's silk. A gentle murmuring filled his mind, like soft lapping waves. His paws traced the etchings on the wood. They lingered on the uncrossed marks, and he felt sadness spike into his pads. These are untold stories...
"We should get back," Leafpool decided.
"What about the stick?"
Thunder rolled in the distance. Wind whipped off the lake buffeting and pushing like a bad tempered badger.
"We must get back to camp." Leafpool sounded worried "I can see the storm clouds coming. We shouldn't be out in this.... Come on!" Leafpool urged...
"What about the stick?" Jaypaw called.
But Leafpool was already hurrying away. "Come on!" she ordered.
There was no time to drag it back to the safety of the root. The wind was tearing at his fur, blowing back his ears. Pelting rain stung his eyes. Ducking down, Jaypaw darted after his mentor and raced back to the safety of the camp.
Page 154-155
Jaypaw lay in his nest and listened to the forest creaking high above the medicine den. The leaves swished like waves upon a shore. But Jaypaw hardly heard them. His ears were filled with whispering. His claws itched as he imagined the earthy scent of the stick....
"Why don't you go for a walk?" Leafpool murmured from her nest. "Before your fidgeting wakes Cinderpaw as well."
"Okay." Jaypaw sat up. His paws ached to be outside. He wanted to touch the stick once more.
Page 155
He lashed his tail, excited by the stormy weather and the thought of touching the stick once more.
Page 157
"I left something here," Jaypaw explained. "I need to drag it into the trees. I want to keep it safe from the lake."
"What?" [Lionpaw asked]
"A stick."
"A stick?"
Page 158
His heart began to pound. He was certain it was gone, and not just because he couldn't scent it. There was a dark emptiness in his chest that told him the stick was no longer here.
Page 159
"Is this it [the stick]?" Lionpaw called suddenly.
Jaypaw charged towards his brother...He knew eve before he reached it that it was not the stick. "Where are the scratches? I told you, it has scratches!"
Page 159
"I have to find it." Jaypaw wandered away, stumbling over the pebbles and debris. I'm sorry. I'm sorry. He felt as if he had let someone down, though he had no idea how or who. His paw was throbbing now but he didn't care. Had the lake reclaimed the stick?
Page 159-160
Suddenly, his paws knocked something beneath the water.
That's it!
Taking a great gulp of air, he ducked his head beneath the waves and grabbed the end of the branch in his teeth. Tugging desperately, he began to drag it up the beach... the stick was so heavy!
Page 160
What in StarClan were you doing?" The branch slapped down in the water as Lionpaw let go of the other end.
"I saw you disappear in the water and I thought you were trying to drown yourself. Then I realized you were dragging this! I don't know how you thought you were going to get it out on your own."
The water lapped around the stick. Jaypaw ran his paw over it, searching out the scratches. He wished the stick was not so big, that he could take it back to camp with him. "Look," he breathed, running his paw over the marks.
"You half drown yourself in the middle of the night for a stick with claw marks on it!" Water sprayed from Lionpaw as he shook himself. "Your crazy."
"I'm not," Jaypaw snapped hotly. "It's important."
Thank you, Jaypaw. We'll be remembered as long as you guard us.
"Come on," he mewed. "Let's get this tucked under a root and get back to camp."
Page 161
But his mind was fixed on the stick, hopefully still tucked safely behind the tree root. He weaved his way toward it, his heart beating faster as he neared it. He reached out a paw. It was there! Still safe.
Happily, he dragged it from his hiding place and ran his paws over it, feeling the warmth of the wood and welcoming the jarring ripples as his paws bumped over the scratches. The swishing of the waves and the murmuring of the wind away. He was aware only of the branch beneath his pads and the sharp etches cut into it.
Page 213
Disappointed, Jaypaw laid down beside the stick and rested his cheek on the smooth wood.
Page 214
The old cat ran a paw over something smooth and pale--a bare branch clasped beneath his twisted claws.
Jaypaw stiffened. My stick!
Page 215
