It would also help to know what you mean in terms of slower - because, for example, if you have your system automatically defragmenting on a regular schedule, and it automatically adds drives it finds, then that might take longer. Scanning for viruses and malware might take longer. running programs might take longer, might not take longer, might take less time - it all depends on what you are doing.
End result - it might, it might not. It might speed it up, it might not.
Any particular reason you don't beleive the computer technician?
For the most part, it will not make your applications run slower, the caveat being those applications that scan the entire hard drive(s) such as antivirus programs, antispyware programs, defragmenting software, etc.
But, logically thinking, if it did do that then all of us would not be having 2, 3 or more HDs in our system (and if you read my signature block, you'll see I have 3 HDs alone in my system).