does cartridge output level affect surface noise?

Stringreen is right. It should be the same. Since you are at the low end of your phono preamp's input sensitivity it is doubtful that you'd ever overload its input.

The only other thing to consider is whether or not using more gain from the phono preamp adds to the noise level. If it's a well-designed unit, that should be about the same too. Also, sometimes changes in VTA and tracking force can have an effect on the groove noise. Happy Listening!

If you use a higher output cartridge, however, your preamp and therefore your ultimate sound would probably sound better. The less your preamp has to work, the better it sounds.

That's certainly true with lower quality phono stages. But the faster transient response and greater dynamic extension of a low output cartridge easily outweigh any diminution in sound quality caused by pulling more gain from a really good phono stage (like the OP's).

That isn't just theory. It's born out by our own A/B comparisons of LO vs. HO MC's, both Benz's and ZYX's, using a top class phono stage. With good quality amplification, the sound quality using the more sensitive lower output version of a cartridge is always better.

Getting back to the original question, as Plato said, the LO cart he's using now will rarely if ever overload his phono inputs. The HO version might, or might not. The only way to know is to try. Every system's gain structure and behavior when overloaded at the source is unique.

I have found that what most significantly affects how signal-to-noise is heard, is cartridge/arm set up and alignment. Since acheiving what has to be perfection, or awful close to it, I am able to listen to old lp's that were unlistenable before. Try getting a Mintlp tractor, and see how much less surface noise intrudes in your lp listening.
Regards, and good listening,
Dan