There are a couple things to consider when going with a gradient in a logo. But first, you should almost always use PMS numbers when designing a logo, preferably from the "Coated" palette for color accuracy. Even though there are multiple methods of reproducing the logo in hundreds of different formats, PMS is an internationally accepted standard that will give anyone in any industry printing in any process a stable, repeatable target for what you want to brand colors to be.
There are limitations to how close you can get to the actual PMS color depending on the method you are using it in, but you can work with those limitations depending on the application and how important matching brand standard is. It is also very common for a major brand to have designated CMYK and RGB values in their standards guidelines to make sure that the conversion to the other methods gets the best possible result.
There is also the consideration of WHAT colors you are looking at. For example, a PMS 072 Orange is not reproducible in CMYK, so to hit that bright of an orange, the printer will have to use PMS colors.
To address the gradient concern, yes, a 2-PMS Gradient can be a very tricky thing. When you let Illustrator create the gradient, it start with 100% of Color A on one side, and 100% of Color B on the otherside, and gradual steps them down to a mid point. When you create this with CMYK or RGB swatches, it makes for a very nice, smooth conversion, but when using 2 PMS colors, the built in method ends up making this weird muddy color in the middle because it wants to fade each color from 100%-0% respectively. It's not exactly wrong, it just doesn't look good.
A lot of designers and printers avoid this because they don't know the fairly simple trick to fixing it. You overlay one color over the other. I generally do the lightest color as 100% for the entire shape, and let the darker color apply the gradient set to multiply or overprint (do NOT use both, it can have strange results) over the solid color. See Below.
I usually do this simple version more when one of the colors is black. If it's for two colors, I will modify it slightly so that you still fade both colors off to 0%, but the majority of the orange bar is at 100%, and I moved the 100% red away from the end so there is a small step that's solid. If you don't it will start stepping down the color immediately and you lose some of the brightness. Like this:
The nice part is that even using the modified gradients, when you convert to CMYK, you usually keep the same brightness and look (although any color combination should always be tested). Like this:
If you can post the rough shape and look you are going for, I can give you an idea of what gradients to use.
Finally, if your customer really wants the gradient, make sure that you have them develop a solid color version of the logo that they will be happy with for screen printing or vinyls or other processes that don't have an option to screen the color. Better to address this concern right away and provide them with a solution than to have to scramble to develop something they will like in a rush because the pen company needs the logo immediately.