No, like the other reply pointed out too - it's not obvious. The first password unlocks the entire partition, the hidden one is just within the "empty" area of the drive. If you write a sufficiently large file while running the OS you could just overwrite and destroy the hidden partition without knowing that you did so. It's also impossible to tell that the hidden parition is there because encrypted data is indistinguishable from encrypted empty area of the drive.

Since Truecrypt bailed without explanation, do you know if Veracrypt also has this feature?

It does. Veracrypt is basically Truecrypt with some new features as far as I've been able to tell.

After TC killed the project (for all intents and purposes) is there the ssme level of trust in VC?

The question always was what kind of attack are you trying to guard yourself against. I imagine top level agencies have a way to crack truecrypt/veracrypt encrypted volumes, but I also imagine they aren't using that capability against just anyone to not show their hand and risk the issue being fixed.

Your parent seems to point out that's not how it works: you've got access to the ful partition either way, meaning you can accidentally overwrite the other partition.

If I remember right, the hidden partitions are indistinguishable from random data on your disk and it was necessary to provide an offset to the first block (or whatever) so it could be decrypted. You could easily overwrite it accidentally because it just looks like free space.