Well, my first rhetorical question: It's 2014, why MS Access? MS SQL has free versions that are much faster and more stable than any MS Access version, I don't see any drawback migrating.
Now more to your question, 32 bit "should" not be a factor. 64 bit apps can talk to most 32 bit apps via an API without much difficulty. The only exception that I am aware of are 32 bit apps that rely exclusively on DLLs for their API -- I don't "think" MS Access has this limitation. It's probably been at least 15 years since I touched anything dealing with MS Access thus my hesitance to be more definitive in my answer. Good luck.
Thanks for your reply. There is certainly no good reason for the company I'm contracting for to be using these datasources.
It took quite a bit of troubleshooting to get CF 10 to work with these datasources so I imagine the same hurdles are likely to be in store.