Can I use a Presta tube in a Schrader rim?
As you mentioned, one of the primary differences between a Presta and Schrader valves are the diameters--with Schrader valves being slightly larger--and therefore the valve holes on bicycle rims are drilled to suit one size or another.

Your foremost concern with using a Presta valve in a rim drilled for a Shrader valve shouldn't be 'movement' of the valve stem, as geoffc suggested, but rather a 'hernia' of the tube through the excess space at high pressure, leading to a blowout.

Most mountain bike tires sit at a low pressure, therefore you will probably get away with it, however, there is a very inexpensive adapter, sometimes called a 'valve grommet', which is made out of rubber or metal and serves to make the valve hole small enough for a Presta valve to fit snugly. It will also not come loose under high pressure, unlike geoffc's 'old tire' solution.