Can using lots of hard drives slow down a system?

Solution
Heyo Deniedstingray

Well, if you have programs running of the HDD's and they're slow, then yes. Otherwise it won't have any affect on your OS experience.
It's not worse than in case of one large drive. In Windows, there's a default option to turn off drives when not in use and that can induce some delay when they are accessed but that can be turned off. Some "Green" HDDs also have that built in so they would produce same effect.