Yes, you can definetely suffocate with a plastic bag. Asphyxiation doesn't seem to be very pleasant, though. One day I was browsing a porn site and clicked on random videos that were recommended to me at the edge of the screen. One of them was an asphyxiation fetish video where a woman was sealed in a large plastic bag with something like a vacuum cleaner. She was panicking hard for the ~2 minutes it took her to fall unconscious.
I never thought I'd recommend anyone to watch porn lol, but if you want to learn about the process of asphyxiation you can search for these kind of videos. You will see how long it takes, how it can be done and if you could imagine going through a similar procedure. Could be quite educative for you as it gives you an idea what you are dealing with.
A plastic bag and hanging are two very different methods that are difficult to compare. While the plastic bags interferes with your breathing, hanging should ideally compress your arteries / veins in your neck transporting blood to / from the brain which will make you pass out from a lack of oxygen in your brain, not in your blood. That's why you pass out faster from hanging because when the blood flow stops, the oxygen flow to the brain also stops immediately. When you suffocate it will take up to two minutes until the oxygen in your blood is depleted causing you to fall unconscious.