The answer is maybe. The controversy here is that some purport that teeth never have to be extracted (see previous topic), and that expansion of the dental arches is the solution.
While it is true that an expansion appliance may provide additional space as the palate is widened, it may not be enough space to completely avoid extractions in all patients. The amount of space provided by expansion is not a 1:1 relationship. That is, if the palate is widened 5mm, it does not follow that the arch perimeter gains 5mm of additional space. In fact, it is much less than that (Am J Orthod 1991;100:421-427).
An expander used on the upper arch will have a very limited initial effect on the lower arch (Angle Orthod. 1977;47:186-192). Any effect may then spontaneously relapse over time. So if there is crowding on the lower teeth, the expander will provide virtually no help in that arch.
Other procedures have been devised in an attempt to widen the overall width of the arches in the canine area, since this is a much more effective way to provide space for crowded teeth. However, this may also be a flawed technique, since it has been shown that any widening in this area is very unstable (Angle Orthod. 1998;68:53-60), and will likely relapse following treatment.
If expansion of the arch is required to correct a crossbite, an expander is likely an excellent treatment choice. A by-product of the expansion is to provide additional space in the upper arch. If that space is enough to correct the crowding, then the only concern is the lower arch. There are other ways to deal with the lower crowding, including a space maintainer while the patient still has some baby teeth, for example. If that does not provide enough space, extractions may be the best treatment choice.