So this is an interesting idea 
I would say no, just because I think that punishing someone for doing evil isn’t an inherently good act, although having Satan as a figure that exists to scare people into doing good is actually a good act. 
I’m curious to see what other people think though and would love for someone to push on my own thoughts on the topic.
Well, if the premise is false, naturally one comes to a false conclusion. And there happens to be just a slight error in your premise.
Satan doesn’t punish people. God does. Satan too will be punished at the end of time, and will be thrown into hell, along with the other fallen angels, or demons.
I hope this pushed your opinion enough. :DD
In the bible (the religion that actually involves the beings of God and Satan and believes in hell), there is no end of time. 
Oh yeah that’s definitely a fair point
Would you think that someone whose sole job is punishing evildoers in good, though?
There is indeed an end of time. I’m a Christian. I’ve been raised in a Bible believing home and attend a Christian where I take courses on the Bible. I do know what I’m talking about. In Revelation, the end of time comes and then there is eternity in which the kingdom of God reigns.
Depends. Someone who punished evildoers could be a good person, could be a bad person. Of course, I believe all men are fallen and sin, so no one can be perfectly ‘good’.
such a coincidence I’ve been thinking about writing a book based on this
Well, I would say no because Satan is also known for pushing people to do evil and so he might want them to do evil so he can torture them later! So I would nope.
I never thought bout that
But isn’t that exactly what God does too? 
Why is it okay for him to do it, but bad of Satan if he does it?
Technically, god punishes people by sending them to Hell but Satan is the actual one you gives to the punishment’s to the fallen souls. In truth, all he does is open the door for fallen souls to enter through the gates of Hell. At least, this is what I gathered from when I was younger.
Biblically, no he’s still very evil.
You’re missing an important point in that he enjoys doing it. He enjoys killing, murdering and destroying things. God punishes them indirectly by sending them to Hell so techinically He’s punishing them however Satan is the enforcer. And technically, he’s always been the enforcer I think that was one of his roles, to enforce what needed to happen. But, like I said he enjoys hurting and destroying things and he’ll do it gladly and that’s all he wants. Destruction. He’s evil no two ways about it.
I fail to see how that’s relevant as long as he only does that as punishment
He purposefully goes out of his way to steal, kill and destroy things Look at poor Job
Ask Tom Ellis (smirk)
He purposely tempts people to do so just so He can punish them. Satan is like a sadist he loves punishing people,seeing people burn.
I’ve been involved with a witchy community with some Satanists… and there are people who think Satan is rad.
I don’t think that they believe that Satan is bad and if there is a Satan I don’t believe that either. I don’t believe anything or anyone is inherently bad or good, it’s kinda a spectrum.
I don’t believe that a god punishes people or rewards people.I do believe there is some sort of higher power but to me that could be one god or millions… I believe that this/these god(s) lets things play out in real life, just watches and isn’t involved. Maybe they help with other issues in the spiritual world, but I believe that most of the help that you get is from beings called Guides.
I believe that “evil” people (remembering that this is a spectrum) are made with the purpose of being the “bad” figure in this life. Of course, that doesn’t excuse their actions but like I think there’s a difference between person and soul. Just because they’re a disgusting human being person doesn’t mean that they have an absolutely bad soul, maybe they are good in spirit form idk.
Satan doesn’t punish people. He’s a destroyer. A thief comes to steal your joy, your faith, and your peace. Satan can’t send anyone down below, only God can. Satan is not in control, God is. Satan hates.
God doesn’t want to send anyone down below. He wants everyone to go to Heaven. God loves us so much. God doesn’t take pleasure in punishing us. But He is Holy. However, He came down in flesh to take the world’s sin on Himself. God is love.
It’s not Satan’s job to punish anyone, only God’s. We are His children.
But if he really loved us, why would he punish us and/or not do anything against Satan if he’s evil?