Will it slow down your computer? No.
I say this as an expert on computers.
You will NOT notice anything different by joining the folding team on FR.
The only thing I caution against is that your CPU will be running max cycles. That means it will run a little bit hotter. It's not a biggie.
In fact, as long as your computer is adequately cooled, ie, it came with a decent fan and heat sink, FAH will actually increase your system's longevity. Most computers fail, on shutdown, and startup, and the cooling and heating of the components, is the #1 cause of failure. Now you can either leave it off all the time, or leave it on all the time... me, I enjoy my computers more when they're turned on... :)
If you want to run it on a laptop, you should scale back the % of CPU its allowed to consume, to keep your laptop from overheating. I was running it full out to stress test my new laptop and it fried. It was under warranty and I got a new motherboard, but I haven't fired up the program since. If I do I would scale it back.