It would be OK as long as the rocks withstand the water flow, i.e., are not dislodged and moved. However, groundcover would do the same job and seems like it would be better for the "green balance" of the yard. Too much stone starts looking sterile or "other planet." But, I don't think we know your exact plan to the final finish.

Problem is since that area gets a lot of water when it rains not sure how well grass will grow there

As long as water doesn't sit for too long after rain it wouldn't be a problem for growing groundcover or other plants. If you maintain the swale profile, it will still drain with gravel, about the same as with plants.

It depends on the pitch of your land. My house is down hill. I did a ditch edging in front of the foundation planting, lined it with weed block and filled it with marble chips. When it turns to the side of the house I just have the ditch edging in front of the foundation planting. It works out very well to carry the rain water from the front, down the side and away from the house