Yes, HDTV would be affected by the same overloading.
The trouble you are having with UHF35, in fact,
may be caused by the NBC high def signal, not by
channel 12.
Things to try:
1. Call the
TV station and ask them to provide you some filters
because of overload you are getting. In the past,
they sometimes have.
2. Buy an attenuator at
Radio Shack that will cut the NBC level and still
allow 35 to be viewable.
3. If you feel like
tinkering, you can make a "quarter wave stub" filter
yourself out of coax cable. See a ham radio book
for instructions.
4. Borrow somebody else's TV.
I wouldn't think yours should overload so easily.
By the way, if you are running an antenna amplifier,
all of the trouble is probably there.