I know vinca is invasive, but will it invade the grass? Is there something
I can do to block it from spreading into the perennial garden next to this
area (short of not planting it?)

I don't believe it will invade your grass - at least not if you mow
your lawn occasionally.

You can easily keep it out of your perennial beds by putting a plastic edge
around the vinca. It's shallow rooted and seems to spread by top of the
ground runners so you can simply clip them if they try to get out or
lift them and point them back in the right direction.

As far is it being thick enough to block weeds I wonder if there is
such a thing???

Good luck!
Dan D. Louisville KY good ole USA