As DoctorOhh said, CC has never downloaded via cable. Its main reason for existence is to replace the cable. If you purchased CC for this purpose (cable downloading), then I suggest you use the email feature in CC's help to ask for a refund.
I have never understood why someone wants thousands of books on a device but that is your decision, not mine. So ...
1) From your other post
Direct connect via USB to Nexus 7 not working, I suspect that you don't mean "download" but instead mean "see". You are correct. CC does not see books in its folder(s) that it did not put there. You can ask CC to scan for books in its folders. See the CC FAQ
I have books on my device that don’t show up in calibre. How do I fix this?.
However, with 6000 books on your device, scanning will probably not make you happy, especially if the books are not epubs. CC and calibre go through a dance to try to match these unknown books with books in the calibre library. This takes time and matching may not work. If your books are not epubs then scanning will take much longer than sending because CC has to send the book back to calibre for metadata analysis.
Conclusion: it is not a good idea to use the cable and CC at the same time. Pick one or the other and stick with it.
2) Your other post mentions a time delay in calibre when you send 6,000 books at once. When you send a book format, calibre copies that format to a temporary file and then (attempts to) update the metadata in that book. This takes time.
A similar time delay will be seen when connecting after transferring the books. Both CC and cable connections transfer metadata to calibre upon connection. Calibre then analyzes the metadata to do book matching and other things like cover regeneration.
3) For me, sending epubs to my device using CC takes around 1/2 second per book. For 6,000 books that would be 50 minutes. I recognize that this is not instantaneous, but it must be faster than all the messing around with cables and metadata matching and the like. Start it and go have a cup of coffee.
Your requirements (thousands of books on the device, compatibility with cabled connections, 'instantaneous' operations) may indicate that CC is not for you. As noted in the beginning of this post and assuming that you bought CC in the last week or three, we will give you a refund. Having a new unhappy user is not worth the price of the app.