There is a deduction on all the acro series---bwo-bwo, bwo-bhs etc. if they are not connected. Basically it means the gymnast cannot pause between the 2 skills. You'll also see the deduction taken on dismount of cartwheel-bt or ro-bt. If the gymnast stops on the end of the beam and then jumps back into the bt, they will not be given credit for the series.
I'm pretty sure a swing doesn't automatically break the connection between two skills as long as there is continuous movement, but on a BWO BHS it would probably result in a deduction like for insufficient amplitude because it would be as fast or strong as a "punching" connection. But you could still get credit for the series IF there was continuous movement between the two skills. From a technical standpoint, the lead up for higher level acro series generally requires an immediate "punching" connection using the momentum of the first skill.
It is possible to swing between a BWO BHS and connect the skills, but of course it is preferable to connect without an arm swing. However, I typically see more of a circling arm swing in the series that are connected with a swing. With the up-down sort of swing, most girls drop their chests forward, which breaks the continuous movement backwards.
I also want to point out that the deduction for not connecting an element to the dismount is nowhere near as large as failing to connect an acro series that starts and finishes on the beam (BWO BHS, etc.). An acro series is a .5 requirement; an element into the dismount is not. The worst that can happen for a cartwheel back tuck is that you can get hit with a rhythm deduction in the connection or the skills are considered unconnected.