I suppose it's possible, but it seems risky to me if your goal is to successfully CTB. I'm not sure what the setup of your car is, so I'm not sure how easy it would be to fully compress your carotid arteries with the method you've described - I'm assuming you would be inside the car during the attempt? If so, then depending on the dimensions of your car, it might not be easy at all. However, what would worry me more would be what might happen if you did manage to compress your carotid arteries.
When you pass out from cerebral hypoxia (which is what's supposed to happen with partial suspension), your body can undergo something called "myoclonus", or involuntary jerking or spasming of random muscle groups just about anywhere in your body. People who watch other people faint often confuse the fainting spell for a full-blown seizure; this is because myoclonus can get so violent that it actually looks like a seizure. Some degree of myoclonus occurs in something like 90% of people who pass out from hypoxia.
Why does this matter here? Well, think about how a car is structured. There's typically only a few feet of space between the ceiling of the car and the floor; you have walls (i.e. doors) all around you that usually come equipped with weird footholds; you're either going to be sitting on or next to one or more chairs. There are a lot of potential points-of-contact from which a lot of parts of your body could convulse in order to generate upward force on your body. And given how low to the car floor your potential anchor point will have to be, it will not take a lot of upward force on your body to propel your neck into a position where your ligature is no longer compressing your carotid arteries enough to maintain hypoxia. In other words, it seems to me that, after you pass out, there are an awful lot of ways for your body to spasm itself into a failed attempt. To be sure, there's a 10% chance that you don't have myoclonus at all, and even if you do, the spasms are random in location and severity; you might get lucky and CTB. But as I said at the top, it seems like you're introducing a lot of extra risk here that I personally wouldn't be willing to take.
But this all assumes that you're hanging yourself inside your car. Maybe you could (i) use the assist grip as the anchor point, (ii) thread your ligature out of the car over the top of one of the car doors, (iii) close and lock the door, and (iv) tie the noose externally? In that case I'd be worried about whether the door could support your weight without breaking or deforming; you'd have to test that out ahead of time. I'd also be worried about the angle of the ligature, as car doors are usually at a >90-degree angle relative to the ground; as a result, you may not be able to generate as much force on your carotids as if you picked another anchor point. And then of course, there's the worry about being seen if you do hang yourself outside your car (though given the existence of windows, that's probably also a worry about hanging yourself in your car, too - do you have a private garage that you know won't be disturbed for at least half an hour? If not, this is a very, very risky plan).
In short: this plan isn't guaranteed to fail, but it's definitely riskier than I would choose for myself. Wishing you lots of care in this difficult time.
