Is it a permeable barrier- does it let water through? If it is, you could leave it down. If it isn't, I'd take it up, or cut 2-3' holes around each plant.

There are 2 kinds of Vinca- one is a creeping (running) evergreen groundcover. The other is an annual, with pink or white showy flowers. They share only the same common name, they are not related- one of the easons to start paying attention to botanical names. The groundcover vinca is Vinca minor, or the larger Vinca major. I'm pulling a blank on the botanical for the annual vinca right now.

The ground cover vinca minor is an evergreen.
Depending on the climate in Atlanta, it is mostly a partial shade plant.
Here in California, the summer temps get very hot, and if it is in the sun, the leaves burn.

Here is a link that might be useful: Vinca minor

Keep in mind that some groundcovers, like the vinca for example, spread by putting down new roots along their stems, so they will need to be able to touch the soil to really get established. Small holes around where you plant will give the mother plant space, but won't do anything for the offshoots.

Also, keep in mind that even most breathable landscape weed barriers get their pores clogged over a very short time. Because the blocked breathable pores cause conditions that weaken and kill living plants, It is not a good idea to use those products.

In my opinion, a better approach would be for you to remove all the weed barrier and in it's place put down 4 or more layers of flattened cardboard (not the corregated type that consits of too much glue, instead use the thiner cardbord type found in shoe boxes and other packaged products. Maybe even poster board often used for science project displays.)

Cover the cardboard with 6 to 12 inches depth of good garden soil where ever you plant each groundcover start. Then cover the entire area with a good acidic shreaded mulch at least 4 inches deep.

Over time keep filling in the voids with more garden soil around the original groundcover start's soil as they seek to send out runners or roots to spread into a dense coverage. Once the groundcover gets established and is healthy, it should competively crowd out all but the most tenatious weeds. As the mulch settles it should be replenished to aways maintain a 4 inch depth.

It is also my opinion, that just like the best way to fight weeds in a lawn is to keep the desired grass as full and healthy as possible, the same is true for desired groundcovers.

http://www.nps.gov/plants/alien/pubs/midatlantic/vimi.htm

Vinca is a non-native invasive species that has caused a lot of trouble in various regions of the US. Above is a link to an info sheet about it. Before planting, please check with your local extension if you are unsure if it may pose an ecological threat to your local vegetation. Unfortunately, many garden centers are still selling it, perpetuating a large problem. You can find lists of invasive plants specific to your region on the web. Educating gardeners is the first step in solving a complex environmental problem.