Can you cook Onions and Peppers by simmering them in sauce in a saucepan?

Use the microwave instead of a steamer (or egg poacher, which is just a specialized steamer).  Put vegetables into a microwavable dish with a cover an add a few drops of water or a little butter. Microwaving steams the veggies beautifully, with no mess. I use glass bowls with glass lids. If your bowls don't have handles, set them on a plate for easy handling when hot.

STOP!!!!!!!!!!!!!!!

Buy an electric "STEAMER".

You can poach eggs and steam veggies at the same time.

I don't, I use it for veggies only, but mine has little bowls in the tray I only realized a few months ago is for eggs.

Yes I dont see why not, my poaching pan is like a small fry pan.

When 'stove' space is limited I've put canned tomatoes & sliced mushrooms in the pan base, then the poaching cups [with eggs] over them, to cook at the same time, its saves space and time especially when using a small stove [like in a camper / caravan].

yes, that is the way I always do it.

Microwave them in freezer bags

An egg poacher? Seriously? You cannot Poach an egg? 

Cooking pepper and onions without a pan? Nuke it. 

Good luck with the mess you will have when finished. 

Egg poachers are meant to produce boiling water and use that to cook the eggs. The difference between them and a frying pan is that a GOOD frying pan has a thick bottm that evenly transmits the heat and also avoids burned spots.

But with the use of oil and stirring constantly, over low to medium-low heat, I suppose you could slowly and adequately cook onions and peppers in an egg poaching pan. But I would not try to cook meat or pancakes.

If you have a microwave, just use that poach eggs.  Put the egg in a microwavable bowl of water, puncture the yolk slightly a few times with a toothpick (so steam can escape and not make the yolk blow up), and microwave for 1 minute to 1 minute-20 seconds .. depending how well-cooked you like your egg yolk.

You can also poach an egg in a saucepan.  Break the egg into a bowl so it is ready to poach quickly.  Add a bit of vinegar to the simmering water in the saucepan and have the water swirling (stir it quickly with a spoon).  Quickly slip the egg INTO the swirling water and cook until it is done the way you want it.

I would never waste my money on an egg-poacher. That is ALL you can really do with it.  And it takes up storage space, too.  Your kitchen will be happier - and will you - with a saucepan, a decent frying pan, and a microwave.

When I was very much younger and lived in a bedsit with just one hotplate I used to put the cut up onions and any vegetables I had to hand directly into the canned tomatoes that formed the base of all my sauces and just simmer them together directly because frying was not allowed and not a good idea given the set up.  You lose some richness but the addition of a bay leaf and perhaps a drizzle of oil toward the end made up for it.  You can make indentations in your sauce to crack an egg into.  Then cover the pan with a lid and barely simmer until the white is set.  Don't wander off your you'll overcook them.  You don't need a separate poacher if you cook them this way.