Yes I definitely think the wrap works for the swinging/jiggling motion.
We have a swing, but if DD is upset to the point of incorporating the 5 s's there is no way she is going to dig being put in the swing. We usually just hold her swaddled in a blanket, tummy-to-tummy and rock, bounce with her while shushing and this works so good!
It took us a little to get the sling down, but now that we do, times that she starts fussing, if I pop her in the sling and walk around she usually calms right down!
The most amazing thing! My sister didn't really by into the calming affect of the sling til this week when she was watching DD and DD was upset and my sis couldn't figure out what else she could want, so she decided to try out my sling and low and behold DD calmed right up and fell asleep! lol My sister was amazed, and I think when she finally has a LO of her own she will be asking me where I got my sling. hehe