Can I slow cook noodles?

If by “noodles“ you mean pasta that comes in the dry form with or without eggs, then yes, you can make that in the slow cooker.

There is one caveat though: other than your meat, which won’t be affected by a bit of extra cooking time, pasta tends to become soggy rather quickly - or, at least “quickly“ in slow cooker time. After 30 minutes, plus minus a bit, the pasta is usually done. So the standard procedure for pasta cooked in the almost done soup, stew or other dish with sauce is to add it around 30 minutes before serving. You might have to add a cup or so of extra water, if the sauce is very thick.

If you want to cook pasta alone, you will have to either bring the water up to temperature first or at least partly calculate the warming-up time into the cooking time. As pasta tends to clump together if cooked undisturbed, you will have to stir at least once or twice, which of course will interfere with your slow cooker’s heating process.
In short, for pasta alone I suggest cooking it on the stove.

You cannot add the noodles at the START, because the noodles will get soggy and make you a very unhappy eater. BUT: You can still eat things with pasta, of course!

This page advises to add pasta just before the meal is done, and roughly double to triple the cooking-time. Be warned, though: Pasta releases starch when cooking! You may not want the starch in your pasta-dish!

So, you may just have to accept that for best results, you will need to set up a second pot and cook your pasta separately before eating.

An alternative option: Rather than slow cook, what you can do is put your pasta in a bowl or pot of cold water in the fridge while you go to work. The dehydrated noodles soak in all the water and absorbs it to the right amount. Then you take it out and boil it for one minute with some salt to get the right texture and it's good to go.

The noodles turn a bit white when you soak them like this, but the boiling water will make the color return to normal. I do this when I have people coming over right after work and I know I'll be needing to cook a lot of things and I don't want to worry about stirring the pasta or checking if it's "perfectly" cooked.

You can, but it does have a different texture than boiled

You will likely find a lasagna recipe in any slow cooker cookbook, and there are plenty on the internet. These use regular dried noodles, not the 'no boil' ones.

If you want to avoid needing to cook ground beef separately, and you don't have a 'multicooker' that can sauté before switching to slow cook, consider making a casserole with diced salami or ham using similar techniques and proportions (and similar thickness of pasta)

My only issue with the slow cooker is that you don't get the browned crunchy top to add some textural contrast, so I'd probably serve it with a more crunchy garlic bread. (Toast some sliced bread, then rub a garlic clove against the cut side)

Note : cooking it in tomato sauce (acidic) will keep it from going soggy like it would if you just put it in water. And there's a limited amount of moisture for it to absorb