Yes. It's the sum of all angular momenta in the solar system, with respect to its centre of mass.
So each planet (and the Sun) contributes something to it, with the greatest contribution coming from the far-off and massive gas giants (Jupiter, mainly).
Let's say we have an unlikely, imaginary solar system with two planets only, each orbiting at 90 degrees to each other's plane of rotation (like one orbiting around the Sun's equator, the other doing a polar orbit).
Each planet's ecliptic is just the plane of its orbit.
But the invariable plane will be the sum of their angular momenta, and be lying somewhere between the planes of the two orbits.
If you then took one planet and just disappear it (Death star-style), the invariable plane would change, but the orbit of the other planet would remain nearly the same, and as a result the average insolation of its surface would not change. Same if you added more planets to the mix.
In another imaginary system, one of the planets could be so massive, and contribute so much of the total angular momentum, that the invariable plane would almost always be nearly the same as its orbital plane (i.e., its ecliptic), regardless of what orbits other small planets would have.
That is to say, the invariable plane is something of a convenient (for some purposes) mathematical abstraction, and its inclination w/r to the Earth's orbit doesn't have that much meaning by itself.
Having said that, it does change, because planetary orbits change. What affects the climate of any given planet are these individual orbital changes, rather what other planets are doing and what is the resultant, particular orientation of the invariable plane.
These changes are extremely slow, though. You may want to look up Milankowitch cycles to learn more how such changes affect climate, and what are the timescales involved.
