Would this do what you want?
customers.Where(c => Array.FindAll(c, str => str.ToLower().Contains(searchText.Text.ToLower())).Count() > 0);
I don't know if it performs any better though.
[Edit]
This is probably a little faster, as it only looks for the first match, enough to tell you if anything is there:
customers.Where(c => !String.IsNullOrEmpty(Array.Find(c, str => str.ToLower().Contains(searchText.Text.ToLower()))));