If you are raising greens, the grass will probably execute them, and you will not harvest hardly anything.
If you are raising melons, they will probably be fine.
In my
experience, the trouble with grass is not so much nutrients but room and shade. Vegetables are more tasty than they are strong, and they simply cannot compete for light and room if the weeds are rank.
Exceptions, of
course, are the really BIG vegetables like squash and such. They seem to be able to compete with everything except Johnson grass, and Johnson grass is not only invasive it grows 5 feet tall.
Gardening is as much an
art as it is a science. If you think that a vegetables looks happy it probably is. If the grass you mention-and I am not familiar with that variety of grass- is not terribly tall then you might have a fine garden even if you have grass in it.
I am, by the way, getting vegetables established in an area that has our big, native midwestern grasses in it. Asparagus is doing fine with no weeding. Chives survived. Onions failed. Squash failed but then half the squash in my area failed that year. Etc. Some plants do well and some do not!