In traffic and at idle I can tell you from experience that a 1966 GTO will overheat without the factory shroud, but it you run a S/S Flex-A-Lite fan you should not have any problems.
As far as the number of degrees...enough to puke out coolant.

 

I just tripled up some tin foil to get my anti freeze stuff to go into my buckets,,not to fancy but it works

 

I installed my new shroud this weekend... I removed the fan, installed the shroud, and then re-installed the fan, and it worked fine. My shroud, however, is really tight on the bottom, and has extra space at the top. It scrapes big time when I turn her over, luckily my fan blades aren't messed up. I've started to cut out the part that scrapes... and I have just a couple more small adjustments tonight before I test her out. I'm excited to report the amount of temperature drop the shroud adds.

 

I have the same fan/shroud issue, the fan has about 3' of space up top and about .5' at the bottom.

Something that was pointed out to me by a mechanic was my engine sits to low in my bay, that or its angled in-properly. Because of this my fan isnt sitting centered in its shroud, that and its not centered infront of the radiator. Infact the bottom of the shroud is all chewed up with chunks missing. Iam not sure if this is causing my heat issues or if my radiator is bad. I just hope I dont need to realign my engine, ill replace my stock radiator before I do that.

 

FWIW, putting a shroud and a new clutch on the fan got me from 240 degrees down to a rock steady 180.

This was on my Firebird's Pontiac 406 but its cooling system isn't much different than a Mustang's.