I will answer your last question
Then how does converting beforehand help?
First - you see what the colors will look like. Not exactly the same as final product but close.
On the left are colors in RGB on the right are CMYK. Add to that the fact that paper can make it more dull and your fresh beautiful green grass may turn into brown pile of brown pile.
Then when you are converting colors you can (and probably will) experiment with different profiles. Depending on the paper, printing machine etc your outcome may differ. YOU will choose what best suit you and what you want to achieve.
Why you should do this? Because then you can print Cromalin or "Proof". Something that will show the colors after printing. This will save you time and money when talking to printer or when making a complaint.
Sometimes the printer will use profiles build in their RIP. They are often set to change CMYK to machine CMYK (for example the machine will add 10% of Cyan so the profile take that 10% from plates). Unfortunately those RIP profiles can ignore strong RGB colors (as they are set to convert only CMYK to CMYK). I've seen prints where almost Green or Blue objects where just very light grey.
Converting beforehand give you also one, often overlooked, profit. You will comply with the Total Ink Limit. Some printers will just ignore the fact that your work is very dark and have almost 400% TIL and will print it. It will
A) warp the paper
B) will need powder to absorb the excess of ink.
It will of course, make printing time take longer and the Printer will bill you for the extra time on the machines, extra work needed to handle the prints and will tell you it's your fault.