What's the relationship between Moon phase and the Milky Way visibility? I've been using an IOS app to predict visibility of the Milky Way.

I'm planning a trip to capture the Milky Way on 9th March 2015, but the app shows the visibility will be very weak on that date.

The Moon doesn't even rise until 9:12am.

Does the Moon phase still affect the visibility of the Milky Way even if it is not above the horizon?
Moon Phase
With the moon phase, it's going to be in Waning Gibbous on March 9th, so it will be reflecting a lot of light back to earth. Any light that interferes with the sky will make dimmer objects harder to see.

The Moon's reflectivity figures taken from here:

Fraction of the moon: 0.61371425766053
Illumination of the moon disk: 88 %

Location
It will also depend a lot on your home location (hemisphere) as to the position of the Milky Way at different times. Your proximity to any light pollution will of course have an impact, as living on the outskirts of a city myself, it is impossible to view the Milky Way. Only when in very rural areas on clear nights have I had a good view of it.
New Moon
On the 20th March there is a New Moon, so this may be a more opportune time to try to capture it.