Will a vortex form if you pump water up via the bathtub drain?

[Swamp Thing]

... And if it won't form spontaneously with reversed flow, then will a vortex at least sustain itself once we nudge it in one direction?

 

[.Scott]

No. A little angular momentum becomes a rapidly spinning vortex when the water flows into a relatively narrow drain. If water emerged from the drain into the basin, any angular momentum would be spread across the basin - and thus would spin more slowly.

 

[256bits]

Summary:: ( Forward Flow --> vortex ) ==> ( Reversed flow --> vortex ) ??

... And if it won't form spontaneously with reversed flow, then will a vortex at least sustain itself once we nudge it in one direction?

You mean if it could be a time reversal phenomenon.
Dissipation effects can probably rule that out to be completely true.