rafters are 24 inches on center

Why wouldn't you?  Not sure I understand why you would question this as most houses have sheathing attached directly to 2x4 rafters.

But on the other hand, why would you?  The boards shouldn't do any harm.  You would just have to use longer fasteners.

...and radiant barriers in attics don't work anyway!  Don't waste your money on the radiant barrier.  Re-sheath with or without removal of the present boards..not a big deal either way as long as the additional weight doesn't present a problem.

http://www.energysavers.gov/your_home/insulation_airsealing/index.cfm/mytopic=11680

http://www.gp.com/build/product.aspx?pid=1398

My thoughts were that doing the project as described wouldn't be a big deal.  I am curious if the 7/16 OSB is strong enough to span the 24 inch on center rafters.  This was really my big concern and I though I would check with some of you to see if I was missing something.  

As far as the comment about radiant barriers not working in the attic to reflect summer heat... is my information in the link incorrect.  The space is finished directly below the roof (finished attic) but it gets unbearably hot in the summer unless the 220 window AC and the 110 window AC are on full blast; then only tolerable.   

I'd like a clarification on Ron's statement as well.  A lot of us think that radiant barriers work, and some claim to know that they do.

Most attic heat is a result of thermal transfer between the exterior face of the roof and the interior of the attic.  Insulation will help that.  Radiant barriers generally have high thermal conduction (e.g., aluminum facings).  They work fine for light emitted heat (by reflection) but less so for non-light thermal transfer. (although there is a significant anomaly in that as well...go out and put your hand on a chrome trim piece on your car on a 90F day...it's hot)

Perhaps my experience is anecdotal....comments please.

My experience is totally anecdotal, but in our hot climate, houses and commercial buildings typically have aluminum foil sarking or aluminum foil faced batts installed directly under the roofing.  Maybe this is the wrong forum for good advice on this.

http://www.energysavers.gov/your_home/insulation_airsealing/index.cfm/mytopic=11680