Yes it would. I do not have the time to calculate the details, but the interstellar medium contains 10 to 100 times the amount of gas, and depending on your exact location, the ambient cosmic radiation fluxes are also hundreds of times what they are near the Sun's distance. The solar system would be frequently invaded by dense interstellar dust clouds which would reduce the amount of sunlight we would receive and probably bring about terrible ice ages. If the Sun passed through a dense cloud with about 1000 atoms/cc, the ionosphere would be eroded, and the ozone layer would disappear rendering us vunerable to harsh ultraviolet radiation. Also, on timescales of only a few thousand years, the stars in our skies would change dramatically, and depending on the mix of stars in the core, you could find yourself next door to some rather nasty luminous O-type stars and supernova remnants. Every few million years or so, you would have a supernova within a few light years of the solar system which of itself would be lethal...but spectacular!