I have also applied for the CA immigration while living in Germany and
I forsee the same situation in my case, therefore I have done some
reaserch on this issue.
All CICs all over the world maintain the same policy about this issue,
its our responsibility to send our passport to the CIC where we have
applied (in your case in the US) and CIC-New Dehli will NOT stamp the
PR visa for you unfortunately.
One more problem current indian laws prohibits sending of passport to
oversees via post, what you can do is, either carry it with yourself to
the US (on tourist visa, its an expensive solution) OR you can send it
with a friend/ relative leaveing for the US, they can send it via mail
to the CIC from the US, moreover in that case, the CIC in the US will
never mail it back to you outside the US, so you have to provide a
mailing address for the passport return back within the US (your
freind/relative address inside the US), then they can post it to you
back in India.
hope this will help