I'd only recommend if you don't mind string-trimming. I don't think the landscaping fabric will be a help here.

But,it need match your yard,it is better post your yard pics here...
{{gwi:47224}}

I was thinking of using the landscape fabric under the rocks to help prevent grass from encroaching into beds. Here are pictures of the beds that need edging. I'd only use the rock along the bed with arbor and the bed with bench/fence.
{{gwi:47225}}
{{gwi:47227}}">
{{gwi:47228}}
{{gwi:47229}}
{{gwi:47230}}

That's gorgeous! But you'd still have long grass growing up against the rocks.

We are having good luck with corn meal gluten to reduce crabgrass. But trenching is apparently better for controlling many grasses. You could put the rock in a trench, and that would make a barrier for the roots to cross. If you want to mow right up to the rock, you have to do something more than pile it. Maybe put down a straight edge timber to cut along, then put the rock on top of the timber.

Fist off - your garden is beautiful !! I would also suggest just making a deep trench to keep the grass from creeping into your flowers. It will also be a big benefit when you are edging/weed wacking in that area.