On a similar note, does it reduce your chances of being funded for the first year if you mention NSF application or private funding like
the OP ... which you otherwise might have been given anyway based on the strength of your profile ..
To be clear, will the adcom say : "Instead of admitting JUST this one guy who might already have funding for first year, let's admit him with no funding and admit someone else with the first year funding. That way, we can bring in two."?