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As long as you don't pass the arguments on to Process.__init__() when you call it there should be no problem.
The following program works, but will fail with RuntimeError if you uncomment the comment line:
from multiprocessing import Process
class Unpicklable(object):
 def __reduce__(self):
 raise RuntimeError
class MyProcess(Process):
 def __init__(self, foo, unpicklable_bar):
 Process.__init__(self,
 #args=(foo, unpicklable_bar)
 )
 self.foo = foo
 self.baz = str(unpicklable_bar)
 def run(self):
 print(self.foo)
 print(self.baz)
if __name__ == '__main__':
 p = MyProcess([1,2,3], Unpicklable())
 p.start()
 p.join()