RMS of absolute-valued sinusoid
Your reasoning is correct. The signal $x(t)=|\sin(2\pi f_0t)|$ is periodic with period $T/2$, where $T=1/f_0$. Consequently, it has components at frequencies $2k/T$, $k=0,1,\ldots$, i.e., at $0$Hz, $2000$Hz, $4000$Hz, etc. Since the ideal low pass filter has a cut-off frequency of 1500Hz, all harmonics are completely suppressed, and only the DC component appears at the output.

I'm sure that you know how to compute the DC component of $x(t)$ (which, if positive, equals its RMS value).

Your concerns about actually implemented filters and capacitors etc. are irrelevant to the question, which explicitly states that the low pass filter  can be assumed to be ideal. But even a non-ideal low pass filter of appropriate order would suppress all harmonics sufficiently, such that they would be buried in noise.