I haven’t fostered, but I have worked with children in children’s homes, so I’ll just add my perspective from that angle.
You’ll always make a difference. In my work we’ve sometimes had children come in from very problematic backgrounds and sometimes they would go back after a fairly short time with us. Even then, it was noticeable that in that short time we had modelled some very good things. So many children grow up with little support and stability and no sense of unconditionality of family. To show them that even a little makes an enormous difference. You can’t magically “fix” children so that they’ll never have any problems and be model citizens forever more, but you will make a difference. There is no way of knowing how children react to anything in advance. There are children I’ve known who’ve seen terrible things and who are perfect now. Beyond perfect: they blow my mind every day. Some don’t come out unscathed, but are still incredible people. Children are so resilient, and they absorb everything around them. Anything you can show them will benefit them and it will not be wasted.
You do have a point: when the children would go home and then come back that was always very difficult, but it doesn’t mean your effort didn’t make a difference.
Bear in mind that it will likely not be apparent in gratitude, or anything like that. (I’m sure you’re aware of that!)
I’ll ask you this though, because that’s always what we wanted to hear when hiring new people: you mention sharing what you have, and that you’re looking for a sense of accomplishment. But do you also want to do it because you want to? Does it appeal to you because it seems like something (for lack of a better word) fun? Challenging fun perhaps, but something you want nonetheless?
If you only want to do it because it seems like a “good” thing to do, I would recommend you reconsider. Do it because you want to. Because you want all of it, tantrums and swear words and picky eating included.