Can I pipe roof and sump water into an unused shallow well?
You can, but it is considered an injection well and is regulated by law:


  In the United States, injection well activity is regulated by the United States Environmental Protection Agency (EPA) and state governments under the Safe Drinking Water Act (SDWA). EPA has issued Underground Injection Control (UIC) regulations in order to protect drinking water sources.


You actually have to get a permit and meet specific conditions in order to operate. Not doing so is actual a violation of federal law. The reason for this is you are putting contaminated surface water into the aquifer, and potentially contaminating the drinking water of anyone else connected to that aquifer. 

This would be considered a Class V well: 


  Class V wells are those used for all non-hazardous injections that are not covered by Classes I through IV. Examples of Class V wells include stormwater drainage wells and septic system leach fields.


You should read up from the link above and on the Minimum Requirements for Class V Wells.



If you aren't willing to do all this (because french drains are much simpler..), you should abandon the well. I can't find EPA regulations on this, but here in Ontario, Canada you're actually required to abandon unused wells under the Ontario Water Resources Act, and I'm sure the EPA has similar requirements about unused wells. Well Aware has a good page on Decommissioning  unused wells.