Any device that can run software can have viruses written to run on it, and any device connected to th internet can have viruses downloaded on it. (I'm still waiting for someone to write a virus that gets transferred over the power grid. Then civilization is in big trouble.)
So yes, you should run an antivirus program. And yes, it will slow your phone down, but not enough to notice unless you're running a benchmark program to see how fast the phone is. (It's like asking whether you should clean the dust off your eyelashes because it's harder to walk with the extra weight. It's there, but it's not significant. An antivirus program runs when you download something and when you're not doing anything else. The rest of the time it takes so little of the phone's resources that it's effectively not there.)
I'd also run
Malwarebytes Anti-Malware. Not all bad stuff is viruses.
