If a secondary HDD/SSD is connected in the system during boot-up it will affect boot-up time. However, the delay in boot-up time as compared with *only* having the boot drive connected can be insignificant - even hardly noticeable - depending upon the PC's power, i.e., processor, drives involved in the boot-up process (SSD or HDD), and the like.
Anyway, there's one way to check it, right? Try it both ways on your PC and see the results.