Certified GKH Gardening Expert
Yes, you can do that. The common form of Creeping Jenny can be invasive in some areas though, so you may want to keep that in mind. The golden variety is less invasive, but still can cause problems. Creeping jenny also only really does well in marry soil, which you typically don't find in cemeteries.
A good alternative would be to look at creeping sedums. There are literally hundreds of varieties available. Many have a similar look to creeping jenny but are not as invasive and are very drought tolerant. They also need little care to thrive. All of these would make them ideal candidates for a gravesite groundcover.