Yes, the ShockStop will work well with the Jones bar for most of the hand positions. In fact, many of our customers use the ShockStop with a Jones H-bar, and it works well for them. It is important to note that when riding with hands on the swept back portion (DH / Upright in the image below) the stem may not provide any suspension at all.
Every position on the bar except the DH position will work well with the ShockStop. In general, swept back bars do not work with the ShockStop because it is a single pivot suspension stem. This means that it absorbs shocks and vibration by rotating about its pivot point. The pivot point is just in front of where the stem attaches to the steerer tube.
Because it is a pivot, only loads that are in front of the pivot point will actually cause the stem to flex (a "moment" is required to make it move). In the DH / Upright position you will not be applying a "moment" to the ShockStop, because all the weight on the handlebar is at a point that is likely behind the ShockStop's main pivot. With hands in this position the stem will just feel like a normal rigid stem.
Now, if the hands are moved to the Rest / Climb position it will be like riding a traditional flat bar and the stem will be able to flex. If the hands are in the aero positions then one will experience even more effect from the stem - almost like riding with a road bar with hands on the hoods.
We always recommend to customers who have a Jones bar that they experiment with different elastomer combinations in order to find the setup that works best based on where the hands will mostly be. This is especially true if using a handlebar mounted bag because the elastomer combo must be set stiff enough to account for some static weight on the bar.
For more information on choosing your elastomer combination, check out our article "How do I choose the right elastomers for my bike and riding style?"