Yes, Bitcoin can.
How? Easy, give enough bitcoins to someone with cancer, he then use them to pay for all the expenses for healing and ta dah, bitcoin cured cancer. Ok, success is not guaranted but it's a start
Also you can donate bitcoins for research on cancer
Someone trustworthy has to be the one who holds onto bitcoin donations and converts them into USD and then donates that to cancer research foundations. Hopefully the money is sent to them in a fees-less manner like bitcoin. Damn you Paypal! *shakes fist*