How will an electric fields affect the formation of plasma sheaths?
A plasma sheath is the interaction of a plasma with a boundary. As long as you let enough time for the plasma to be created, you let enough time for the plasma to create a self-consistent electric field in the sheath. In stationary plasmas, the only case when there is no sheath, is when the surface that the plasma is in contact to, is at the plasma potential (i.e. same potential as the plasma), which means you have to supply current to this surface (in Langmuir probes in DC glow discharges, for example) in order to compensate for the fact that electrons arrive more quickly - and hence, at a higher rate - than positive ions, to the boundary, producing a net negative charge flux and thus a current. And in this case, there is no electric field either.
In all other cases, the sheath is necessarily accompanied by an electric field of its own, because the electric field is what allows the sheath to exist, as an entity with different properties and structure than the plasma bulk.
If you increase or decrease the electric field applied to your discharge, the sheath will change, and adapt to that field. Basically, if you try to increase the voltage in a DC glow discharge, the cathode sheath will first cover all of the cathode area, then the current across the sheath will increase to allow the potential drop across the sheath to increase. Then the cathode will heat up during the transition to arc, and the sheath will change to take into account the increase ion and electron emissivity of the cathode. All these processes are rather complex and depend highly on the situation.
So I think one might say: sheath and electric field are bound together by many relations, so it is difficult to answer without knowing a little more about your particular case!