Realistically, no. It does matter in the sense of, whether it provides suitable tuition and facilities for you to develop as an artist. It doesn't in the sense that, if you "make it" in the art world it won't be on the back of a degree name, it will be due to networking (which, a more well-established course may help by having more situations where you can do this) and on your own abilities (which are only supported by the course, not completely made by them).
You enjoying your environs and the course will have more of a positive effect on your work in the degree, and hence on the quality of your portfolio, and hence your applications to any particular roles related to design, than the name of your university.