Sure, extremely plausible.See the link below for more information on the dance The Spanish Gypsy (or Jeepsie), the song from which the tune for the dance came, and the 1623 play from which the song came, which had the title "The Spanish Gypsy".
I'll go out on a limb and make some historical pronouncements which cannot be proven, but which seem most probable to me:
The dance title The Spanish Gypsy came from the dance being done to a tune associated with the play The Spanish Gypsy.
The dance figure Gypsy got its name from the prevalence of the figure in the dance The Spanish Gypsy.
I think you're saying that Cotswold dances as collected by Sharp and others reflected Elizabethan country dances as shown in Playford, and that whole-gyp and half-gyp were therefore originally named after the (notional) country dance figure and were thus properly named whole-gypsy and half-gypsy. Please correct me if I've misunderstood this.The Morris dance figures whole-gyp and half-gyp were originally called whole-gypsy and half-gypsy. (Although parts of England had and ancient tradition of seasonal dancing under the name Morris Dance, it seems likely, from the nature of the dances, that the form of the Cotswold dance traditions collected by Cecil Sharp only went back to the Elizabethan period.)