Hi Lucas County, probably, yes, but that would be a big project to dig a trench or use a trencher like the utility company uses to install a barrier.  

First off, though, is do you really have "Wiregrass?"  I looked it up on google and it is bermuda grass in the south.  It should not be able to grow up here but with global warming, it is now growing in various places in the state.  The best possible thing for you to do is to take a fresh sample of the grass to OSU Extension in Lucas county during normal business hours and have them identify it for you.  It makes a difference as to what herbicide you can use and what will work and be effective.  

As for the bare ground between the fence and the flowers, it would be a good thing except you would have to apply the herbicide a couple of times a year to make sure it was under control.  Wear PPE  - chemical gloves, long pants, boots, long sleeved shirt -- when you spray the chemical.  Wait until you can have no wind to drift onto your desirable plants.  Fall is the best time of all to spray since the plants will take the herbicide down to the roots to kill the entire plant.  Also, if it is Glyphosate (Roundup or equivalent) the plant has to be actively growing to take the herbicide up and get killed.  Usually, if you get the spray on the leaves and it dries say in a couple of hours, it will work and start the kill.  

To sum up, I would take a fresh sample of the roots and long runners and flower spikes as well to the OSU Extension office in Lucas County and ask them to identify it for you.  Then attack the no grow zone.  Also, another method on the label for Glyphosate is to fertilize the plants in question with a high nitrogen fertilizer say something like Miracle Gro for lawn which is high in Nitrogen.  It will stimulate the plant and then a week to 10 days later you spray with roundup and that is the end of the weed.  Hope this helps you.  Don