EDIT : I have added some more detail to my answer in response to the OP's comment.
To answer your first question:
Yes, it is theoretically possible to use a solar sail to place a spacecraft on an escape trajectory from the solar system. The key to achieving this is to have attitude control sufficient to place the sail at an oblique angle to the sun nadir direction. This would allow some pro-grade or retrograde force to be applied with a necessary force component in the radial-out direction. Doing this at around the same position over subsequent orbits would allow for a slow growth in the orbit size. It would require changing the attitude of the sail such that its surface was perpendicular to the radial direction during the "non-thrust" time spans such that the cosine factor goes to zero and solar pressure becomes minimal. The most optimal process for this will shift as the orbit becomes more eccentric, but it is entirely feasible as a source of useful delta-V on orbit.
To answer your second question:
There is no theoretical mass limit for this process. With a sufficiently large sail, or a sufficiently long mission time, any mass could use the same process with varying accelerations. Currently designed sails are on the order of 30-40 square meters and are intended to carry cube-sats, but only as test bed's for future sail implementation. We are many years away from an interstellar sail.
The force exerted by solar radiation pressure on a solar sail is roughly defined by the following equation:
$F_{net} = 2A_{sail}\frac{I_{f}}{c}cos^2(\alpha)$
Where $I_{f}$ is the incident irradiance, c is the speed of light in a vacuum, A is the area of the sail, and alpha is the angle the sail normal makes with the sun radial. An object orbiting around Earth is at approximately 1 AU from the sun, and therefore experiences a solar irradiance of 1.361 kW/m^2. For ease, I'm assuming the sail is square on to the sun, meaning maximum pressure and an alpha of 0 degrees; this takes the cosine factor to 1. Given these assumptions, the Force exerted by the sun on a 32 square meter sail is about 0.29 mN. This is an extremely small force, equivalent to 1/15000 of a pound. The benefit is it can be maintained for long periods of time, especially once the orbit is highly elliptical, and the craft doesn't need to carry large amounts of fuel. It is safe to say that the maximum useful payload would be on the order of just a few kilograms, but you can always put a heavier payload with reduced performance given enough patience. The force is directly proportional to the Area, so doubling the area would double the payload capacity.
There IS a mission focused on launching a solar sail. There was a failed attempt in 2015 due to deployment and system issues, but they are scheduled to make a second attempt later this year. This particular mission uses a 32 square meter sail with a 3U cubesat (about the size of a brick).
