I assume that you refer to our finances and not our playing staff when you call us "the most thinly resourced team in the SPL". We might pay the smallest wages and have one of the smallest home gates but we do appear to a have a bigger and stronger squad than some of the teams around us.
Teams with thin resources have done it before. Since the turn of the century the following non-OF teams have qualified to represent Scotland in Europe:
Hearts (3 times), Aberdeen (3), Kilmarnock (2), Dunfermline (2), Hibs, Livingston, Dundee Gretna and St. Johnstone.
Teams of our size (and smaller) do qualify for Europe and i'm sure we would do lot better than the likes of Dunfermline and Gretna if we got our chance.