Yes, tosylates can handle a column just fine. I've never tried a alumina column with it, just a standard silica column.
However, polymers usually smear all over the column, so pay close attention to your TLC.
You should try precipitating or redissolving in various solvents and see if you can't get purification that way. For instance, tosyl ethanol is probably soluble in diethyl ether, but polymers tend to have terrible ether solubility.