Rebuilding a 10 year old mt bike for your tour is a better idea than the cheapo bike on ebay.
My gf rides one with a rigid fork and she really likes it on pavement. It works well on dirt roads too, as long as they are reasonably graded. Pot holes and wash board roads will be tough on any bike, including one with front suspension.
Is this charity ride financed in advance by you and 100% of the donations go to charity?
I've heard of people skimming off the cost of their tour and then giving the residual to charity. Shame!