I'll assume that you are asking about this because you are actually making several of these at the same time, and want to stack up the steps. This is often done when when mass producing things like cutting boards. They are often sliced, planed, and jointed from larger chunks. [And I see from your last comment that this is exactly what you are doing.] Of course, these sorts of shops (factories, really) probably also have power feeders and other conveniences.
In this case, the edges will often not be actually run through a jointer. To handle complicated grain patterns, most high production shops will use a higher RPM tool, along with with multiple carbide cutters. They treat the wood more like soft metal, trying to throw off tiny chips. In most cases this will be some sort of routing tool, probably with variable speed and a pretty high top speed. The profile will be cut into the edges with and across the grain reasonably well, though there is often a finish sanding step required because of tear-out.
You also have to accept some number of items that have to be discarded because of tear-out or whatever.
If you do need to use a jointer, I suspect a much higher RPM unit with higher numbers of carbide cutters is what you want. My advice would be try with fresh cutters, taking very light passes.
To answer your main question: is this safe? Well, you are risking a variety of kickback situations, especially at higher speeds. I'd wear a full faceshield and stand well away from the line that the tangent to the cutters makes with the material. And, as I mention earlier, take light passes. Remember that the primary job of any router or jointer is to remove the meat from the unwary operator. Make sure you use feather boards and so on to keep yourself safe.
I bet you could even rig up a jointing or routing jig to make things safer. Since you are doing large numbers of these, a jig might save you time in the long run.