Answer really depends on the width of your rim's (where the brakes line up.) Very few 'cross bikes actually come with rims wider then standard road rims these days, so you'll likely be fine. If you want to be sure, find out the rim width of the Alex rims and whatever road wheels you'll be using.
FWIW, my 'cross bike doubles as my winter trainer. I race on Ksyrium Elites with 35mm tires during the cross season and run cheap Ritchey wheels with 25mm tires for the winter months and on wet days during the road season. I don't even have to think about adjusting my brakes.
Last edited by bitterken; 02-22-08 at 04:01 PM.