Could be, but I think it highly doubtful the books will play out the way the show does - there's just way too many inconsistencies between the two at this point.
The Knights of the Vale showing up was still completely stupid for two reasons. First, it doesn't really seem that very much time has passed since Sansa wrote to ask Littlefinger for help. Mobilizing such a large force as they were made out to be and moving them from the Vale to Winterfell takes quite a bit of time. Checking the
interactive map shows that it's almost 1500 miles from the Eyrie to Winterfell by land.
Your average medieval army could move something between 5-10 miles per day. Assuming that this was a fully mounted army on a death march that still somehow managed to keep itself well supplied means that if they were 100% ready to go when they got the call for help, they'd still have to do 2 months of uninterrupted marching.
Second, the first book states how easily you can oversee the surrounding landscape from the towers of Winterfell when they see Robert and his entourage coming. They should have seen the oncoming army of mounted knights at full marching speed hours before they got there. Even assuming that Ramsey was super rash and just feels that he MUST face his enemy in the field while having no battle experience, he still would've had generals and officers who'd post sentries and send out scouts to make sure they'd not be flanked and to survey the battlefield. The knights of the Vale couldn't possibly have surprised him.
And Jon has been the commander at castle black and has seen battle before. He knows he's responsible for his army. While it wouldn't have looked so heroic on TV, the smart thing to do if he HAD to try and save his dumb brother would be to send a squad of less important people to ride ahead and get him. Just say "You three, go get him now!"
As the commander, he is literally the most important person in that army. He should've known that Ramsey would probably try and do some shit to Rickon to provoke him into an illogical response.
And the night before the battle?
Sansa: "You don't have the numbers, you really can't win this battle."
Jon: "I don't care about that, this show now operates on anime logic and shit will work out fine because I'm the good guy and I'm really determined!"
Sansa: "Dude, you're not making sense. He has superior numbers and a castle!"
Jon: "But that's MY castle and I believe in the heart of the cards!!!11111"
I know I'm way overthinking some of these things, but if the showrunners won't, who else will?