How do certificates work in RWBY

In RWBY Vol.4, Team RNJR kidnapped Qrow?

Not at all

Generally speaking, most people want to survive. As such, they don't mind being brought to safety and medical treatment if they are terminally ill, and expect this in general. This could change now once the person has made it clear that they are dying would like to - but nothing like that happened here. Qrow has expressed no desire to die and was actually poisoned while trying very hard to Not to die. It would be a little perverse to deny this obvious impulse by letting it die and moving on.

Besides, he's not passed out all the time, either. It is especially noteworthy that he has enough time to "heroically" tell them to leave him and save themselves, and not, probably because he knows that if he lives, their chances will be better in the future, and that he doesn't hold her back much. If he had objected, he would have said so and instead congratulated them:

Qrow: It's quiet. Nice job, kid.

Nor are they just wandering aimlessly: they are trying to get to Mistral (specifically Haven, as you suspected), which Qrow had previously (i.e., after they were injured but before they knew about it) advised them to continue.

Qrow: So we're on our way to the headmaster. I haven't heard from him in a while, before the attack. I hope he has the answers.

Given that this is a kingdom, chances are they'll be treated better than Team RNJR can do on their own. Their trip to the ruined village is pretty logical too: if they find medicine for Qrow and keep him alive until they reach Mistral, everyone wins.

Nor, to substantiate this, is Qrow showing a grudge that RNJR spared him. But on the contrary:

Qrow: Hey, am I usually not the one to save you?

Lucy

I'm still a bit confused, in one scene I might have to look it up, he was out for a walk and obviously came around at some point, but I figured she shouldn't check that out because he was planning on staying here. Didn't he want to go?

Lucy

Unyielding

@Lucy - He's been chasing her for days or weeks to keep her safe. He didn't just want to go! And even if he had wanted to, the injury would have changed his plans.

Unyielding

@ Lucy - He was just taking a walk! He said that himself. Again, he would surely have preferred to stick with the dying, even if he had planned to go elsewhere. Generally, when a person who buys IRL is given groceries, has a heart attack and is rushed to the hospital, they are not angry that they did not have to wake up and get their groceries.

Unyielding

@Lucy - If you have been poisoned and passed out personally, would you prefer people to take you for medical attention or just walk around you?