Not maybe. 'You,' the thinking part, are a brain, and 'your death' is always and only brain death. CO enters through the lungs and is carried on through the blood stream, reaching the brain relatively fast... though all body parts will basiclly suffer equally - but the brain is the one that counts as it regulates and coordinates all the rest.
The brain is also the organ that consumes the most energy and the most oxygen (O2, which is now being replaced by CO), so the brain is sure to suffer fastest.
'Arm death' or 'liver death' or even heart death' will never really be the death of you, before the conscious and subconscious parts of 'your brain' fade out - which is of course exactly what you desire. Death by CO is literally 'loss of consciousness' and feels like that, too.
There is no other way to die, the way we define it - all the rest of the organs failing will only cause the brain to fail in the end.
The assumption that there is any other final death for any animal, in this case the human one, than brain death, is a misunderstanding.
When doctors claim that someone died of a heart failure, then they are describing the cause that LED to brain failure, as brain failure as cause of death would not be descriptive enough for bureaucratic or police use.
Btw I had a similar experience like the two car fans, who had acquired an older model Benz that still produced ample amounts of CO, with a generator... my knees started to give and I realized it and barely got away. That experience got me interested...
There was no bad feeling at all, as no hardwired brain alarms (that would cause fear or flight or pain) are being set off.
No nausea, either, just a bit of vertigo maybe, which passes quickly.
I can honestly recommend it ;)