https://arxiv.org/pdf/astro-ph/0001272.pdf
https://arxiv.org/pdf/astro-ph/9904401.pdf
When you see figures like "1E-7 to 1E-2 M⊙ mass range" (from the above paper's introduction), note that a Jupiter mass is about 1E-3 M⊙---one thousandth or 0.1% the mass of the Sun. Earth is 3E-6 M⊙, the Moon is 3.7E-8 M⊙, and Pluto is 6.6E-9 M⊙; or 0.00037%, 0.000004%, and 0.00000066% the mass of the Sun respectively. Compared to stars, planets comprise a tiny fraction of the mass of a galaxy.
TL;DR - No, that's not how gravity works, but you can still ignore the planets in between because they're tiny.