Yes, but that's only true if the designer's monitor is adhering to the international colour standards. That's where calibration comes in. Once the designer is calibrated, then they have ammunition in any arguments that inevitably arise about print quality.
If a designer's screen isn't calibrated, and they get a print batch back from the printer, and the colours aren't what the designer wanted, they don't have a leg to stand on, you see? They don't know if the printer messed up, or if their own screen is wrong.
Once they're calibrated, they can be confident that their screen is right; therefore they can take proactive steps to sort out the printing problem.
This will usually involve correct use of CMYK profiles, but that's a conversation for a later time. I won't discuss that now.