I identify as Israeli and I think it could help me. And if I don't do it, I can never go to Israel without being drafted or straight up arrested.
I had the same problem with Poland actually, military service was mandatory for all able men and I think it still might be, although it's on the cusp of changing for the better. I hold a Polish citizenship, so technically I had to go through this too.. The thing is that I was always even more technically exempt since I was attending university.
Doesn't matter, uniformed men would show up at my grandparents place every once in a while and demand that I show up for training (or bootcamp or whatever) lest I be thrown in jail and charged with some anti-state BS crap. My grandparents got a bunch of official letters stating all that as well - I have one in storage - to frame and put up at some point
I was afraid of coming to Poland, but then eventually I become too old for them to care about me serving in the military and I was able to go to the country with no issues back in 2004. Or maybe it wasn't the age that did it, maybe the paperwork just got messed up? Or somebody figured out that I was actually exempt? Who knows.
Are you sure they'd really give a crap about an American serving in the IDF? I mean, I don't really know anything about this, but if you don't even hold Israeli citizenship (right?), then.. you can probably skip this thing and not worry about it. Then again I'm sure you've done the research so you know better than me, I guess
edit: I see that you're a dual citizen. Still might be exempt like I was maybe? Do you attend university? I realize Polish and Israeli rules will be different, but surely people studying out of country are exempt from this - it only makes sense.