Nope, and I can't imagine how it could! A wider rim will allow the use of more air pressure while helping to maintain a flatter footprint. More air pressure will also help stability. I run 20-21 lbs in my 9"x30 Hoosier lightweight radial slicks. Bias ply slicks may like less air pressure. (Radial slicks are more sensitive track condition and while they may be a little bit faster, they will not be as consistent under marginal track conditions as bias ply slicks.) Stock class racers are limited to 9" slicks and many launch VERY hard. (i.e.: 1.30 - 1.50 60' times with the front wheels in the air.) Many use 10" rims with the 9" slicks. Some have to compromise due to wheel well & suspension clearance issues like yours. Just because a slicks were called "wrinkle wall" doesn't mean more is better. Excessive wrinkling using narrower rims & lower air pressure can degrade the strength of the sidewall and reduce the slick's effective life. The deformation can also extend to the tread and reduce the contact area. Adding more air on a narrow rim will simply reduce the contact area and increase wear in the middle.
But you are correct about the importance of testing & safety. Each car/combo is different and you have to test to see what combination of air pressure & suspension tuning that particular vehicle will like the best.
As noted by flyfish, tire section width is based on a standard rim width the manufacturer uses for a particular tire size. Wider or narrower rims will alter that section width accordingly.
Have you considered a 3/4" offset kit for the leaf springs. That would be the simplest way to get a little more clearance with re-welding only required for the spring pads. (On second thought, I guess the 3/4" kit wouldn't work in your situation.)
You don't need to change the drums unless you want to save a little weight. They do not cause any clearance issues.
