My bike interchanges with minimal adjustment between its CX wheels (Open Pro) and its road wheels (Neuvations). The rim widths are quite similar though. If your road wheels and Alex's are different widths, you may have to adjust your brakes. Determine if this is the case, then you'll have your answer.
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.
bitterken, im guessing that theres no problems with mounting a 35mm tire onto a road rim? the reason I ask is because i have rims with an inner width of about 14mm and i was wondering if a 35mm tire would be too wide for it.