Undoubtedly, those shoes are made for "two hole" or MTB type cleats, which are the type of cleats used by the egg beater pedals, so you should be good.
My only advice is that if you're going to the bother of getting cycling shoes with cleat pedals (which are good things) why you would want one with laces. To me, the biggest hassle and danger of non-cycling shoes is the laces. That's actually the main reason I bought my first pair of cycling shoes 15 or so years ago, to get rid of the hassle of keeping laces out of the chain wheel. I really don't understand why anyone would by cycling shoes with laces or why they even make them. At least get shoes with some sort of lace covers, but better yet, avoid the laces altogether.