Answer
Yes, the gravitational force may be reasonably ignored.
Work Step by Step
As requested, calculate the ratio of the 2 forces.
$$\frac{F_{grav}}{F_{electric}}=\frac{GM_em_p/r^2}{ke^2/r^2}=\frac{GM_em_p}{ke^2}$$
$$=\frac{(6.67\times10^{-11}Nm^2/kg^2)(9.11\times10^{-31}kg)(1.67\times10^{-27}kg) }{(9.00\times10^9Nm^2/C^2) (1.60\times10^{-19}C)^2}$$
$$=4.40\times10^{-40} $$
Yes, this ratio is so tiny that the gravitational force may be reasonably ignored.