Wheel offset has nothing to do with the diameter, or the width. It depends upon wheel design and can sometimes be different front to rear.
Anything over e30 (Bundts), or below e11 (early AMG) could effect steering and handling, judging by what others have mentioned about the zero offset steering of the W116.
Most modern wheels have an offset well above e30 and will therefore rub on the inner guards, or suspension. Spacers can correct this issue, but are illegal in most states and can cause overloading of the replacement (longer) wheel lugs, wheel bearings, or stub axles.
BTW it's ok to have a sleeve fitted to the inside of the hole in the centre of a wheel, as it's essential that the centre hole is the same diameter as the hub spigot. Otherwise the wheel lugs will carry the weight of the vehicle and can fail under this excessive load.