Will this program slow down my computer?
NO. The software runs in the background, using unused CPU cycles and not interfering with or slowing down any of your regular programs.
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.
The short answer is "no".
The long answer: Assuming you're running Windows XP--hit ctrl-alt-del to access the Task Manager. Click on the "Processes" tab. Under the "Image Name" column, you should see a "System Idle Process"... for the vast majority of users, these will be in the high 90's. That's because CPUs haven't been the bottleneck in computational speed for the average user for a loooong time...