It would work, briefly, until the vacuum in the cask would no longer be overpowered by the pump. So, you'll need to put a connector on the gas side of the corny with a short piece of hose to let the air in.
Speaking of which, the problem with casks is that the air gets into them as you serve them. So, either you serve it quickly or you the beer goes bad. Unless you hook up just a wee bit of N2 on the gas side to act as an inert replacement for the beer. But now it all gets tricky and more spensive.
Also, to be a true cask conditioned ale make sure you let the beer carbonate itself, no CO2, no sugar. And finally, most fridges will run no warmer than 40-45. Cask ale is served at cellar temperature, ie 50-55. So you'll need an external controller.