Cougar – nope. Maybe it works like that now, but it never used to.
My HTC Desire was my first smart phone & when I first set it up I didn’t have a Google account. Upon initial set-up it gave several options about where to store the contacts & I chose phone.
I then realised I should probably sort out a Google account and once it was done I tried to see how to get all my phone numbers onto Google contacts. There were loads of threads about it online and there was no easy fix to get contacts from the ‘phone’ to Google. Real ball ache…and annoying, especially as it synced if you added a contact to your Google account, but not the other way round.