I'm guessing that this question arose because you noticed that feeling full after eating is linked to needing to poop. This is because in an simplified model of your digestive system, there's your stomach, your small intestines and your large intestines (which includes the rectum, where poop is stored).

Often, when we eat a meal, the last meal is still being digested in our small intestines. When we eat a new meal, it is likely to spend around 2 hours in our stomach, after which point the partially digested new food will move into our small intestines. So that this can happen, it's necessary for there to be space in your small intestines, so eating a new meal sends messages to your digestive system to ensure the old meal moves along into the large intestines, where the final stages of digestion can happen and the mostly digested food is processed into poop, which gets stored in the rectum. Basically, you can think of it like a conveyor belt, that starts moving when something enters the stomach.

If you put poop up your butt and into your rectum, it would probably just make you feel like you needed to poop, especially if there was an old meal slowly making its way through your intestines. The short answer is that the systems that produce poop are connected to but distinct from the parts of your digestive system that processes food. Your stomach is the place where food goes, so parts of your body that are listening out for a message "we have recently eaten" are expecting that message to come from your stomach (or possibly your blood, because of nutrients being absorbed from early digestion).

That's the simple answer, but the complicated answer is that feeling hungry is actually, weirdly separate from whether we are full or not. For example, there are receptors (special messengers that watch out for certain signals) in your stomach called stretch receptors, and they can detect when your stomach is full. They are one part of the system that helps you tell when you're full, but it's not a super quick system. This is why it's possible to eat too much and notice until a while after, when you feel sick. It's also why drinking a lot of water can make you feel bloated, but it doesn't necessarily make you feel not hungry.

But feeling hungry isn't just determined by your stomach. Have you ever eaten meals on a particular routine, and then switched to a drastically different routine? I started a job where lunch time was relatively early, and I didn't have time for breakfast in the morning, so I decided to have my lunch be the first meal of the day. For the first few weeks, I was hungry all morning, but then gradually, I started to only become hungry when lunch time was approaching. Our bodies are incredibly adaptable, but they really like routine. This is especially significant when we look at hormonal control of hunger. I'm a scientist who studied some of this stuff at university, and the honest answer is that what makes us feel hungry is really complicated and we don't actually understand all of the little systems that work together to coordinate hunger.

The short answer to your question is no, because the rectum being full isn't what tells us we're not hungry.