Apache answers all HTTP requests on DH machines (remember that they are SHARED Servers) so unless you could redirect to mongrel from apache (and as far as I know mongrel doesn't work like that) you're probably not going to get the behavior you want.
NOTE: The terms of service frown on persistent processes.
Of course to really know the answer would require you to post a support request. If you do, please post the answer here.
(I'm not a DH employee)
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