I think this will really depend on one major factor. Exactly where your crew member becomes incapacitated.
If for example they are at base, the chances of having another crew member on 'standby' at the airport are fairly high. In this case there may not be a delay at all.
However if your crew member becomes sick down route at an airfield which does not have based crew your stuffed!
How long the delay will be will depend entirly on how long it will take you to get a replacement there. On long haul this can be quiet sometime whereas with regional it may only be a few hours.
The problem with an agency pilot is that although they would be as fully trained on the aircraft type as one of your own, he/she would not be famaliar with the company Standard Operating Procedures. As most accidents are usually a chain of events which on their own would not prove fatal even this would be seen as degrading safety standards. Of course if your at 39,000 feet and your crew memebr becomes incapaciated then, Im sure the remaining pilot would be grateful for a hand if one should be sitting down the back!