Given the image you posted, if the question is if that exact color is in the gamut of any outdoor signage-type inkjet printer...
The answer is no.
However, you may be able to get close enough to satisfy the customer.
The right track is to not 'convert to CMYK' before printing, but to send the RGB file to the RIP, and let the RIP do the conversion to the printer profile -- which will be CMYK or some expanded colorspace including colors beyond CMYK. Unfortunately though, there's no expanded colorspace out there that's going to get you anywhere close to that green. These days for outdoor signage, all you've really got in expanded gamut choices are red and orange, which are not going to help.
And the old green enhancements -- such as the CMYKOG in the old Epson GS6000, weren't nearly that bright.
So you're probably going to be printing to a CMYK inkset, but profiled correctly, some can come pretty close. (Remember, rule number one is that there's no such thing as simply "RGB" or "CMYK.") I ran this image through several profiles I have on hand, just soft-proofing, and some of them came close enough that I'm pretty certain a client would be happy enough with the result for a yard sign.
Some, and those include the Adobe CMYK default, SWOP, yeah, they won't get it done.
Understand though that this all has to do with how well a printer is profiled and how much of its capability a given profile yields, so where you are your mileage may vary -- a lot -- but I can say that properly profiled on glossy stock, the machine that has the inkset that will come closest to hitting this color is the Seiko/Oki M64S. Its inkset just so happens to be strong out to blue/green.
You would need to use or have access to an inkjet printer that has extended process colors I.e. has a cmykog ink set (I believe Ricoh and others have that capability) or ask your ink vendor if they carry a lime green ink cartridge for your printer that you can use to replace one of your cmyk inks for the job.
Not really feasible in inkjet, Gordo. It's a different world. Inking up a unit and printing a specific color just aren't viable everyday options. "Spot colors" has something of a different meaning, and all colors come from the process mix. That's why every job is a CMYK job.
Pretty easy fix. Just convert the printer to RGB instead of CMYK.
I'm really curious how such a thing would be done.
Mike Adams
Correct Color