|MadSci Network: Astronomy|
A very interesting question. My initial reaction was "Yes, it will change a little" but I couldn't immediately tell by how much, although my initial hunch was that the year would lenghten. This is because I was immediately put in mind of the tidal effect experienced by our own moon which causes a gradual increase in the moon's orbit and orbital period.
The very next thing I did was to note down the effects I thought may contribute to the phenomenon and set about researching each one.
Solar Mass Loss;
Frictional losses and radiation pressure (solar wind);
Planetary perturbations; and
Galactic effects (interaction with the interstellar medium).
and all of them are very small compared to the mass of the sun and earth so their effects are tiny and may not even be measurable. For example, as the sun becomes less massive by throwing matter and energy into space the gravitational attraction between the earth and the sun must diminish. So although the millions of tons lost might seem a lot, it's very, very, very small compared to the mass of the very, very, very big sun.
The most significant issue is tidal losses and you'll find a good explanation in (surprise, surprise!) the MadSci answer. This answer relates to the sun-earth distance, but this is intimately linked to the length of the year.
The other aspect which might interest you, and may even be what gave rise to your question is that there are different ways of measuring the year and although they are all about 365.25 days (disregarding religious years based on the moon), they are not exactly the same. How might this be? It depends on what you consider to be the unique point which marks that you have completed one orbit of the sun, e.g., a geometrical point in the orbit or a return to a particular alignment with the stars. As the plane of the Earth's orbit is rotating very slowly, a point in the orbit such as the perihelion (closest to the sun) moves just a little very year. Look at the US Naval Observatory's explanation of The Seasons and the Earth's Orbit---Milankovitch Cycles and the Wikipedia entry for the year for more information on this aspect.
Try the links in the MadSci Library for more information on Astronomy.