Long and short... No. Putting your leather in the washer and dryer will not achieve your purpose. You might get the affect, but you also may do irreparable damage to the leather.
Water can be an enemy to leather and strip away many of the natural oils the leather needs to remain supple. One of the most critical time in the production of leather is the first stage in which the leather is dried to stop the decay process. This is the "curing" process. Most of the time to achieve and preserve the leather, they are salted, the leather is later soaked in water to remove the salt, and then treated with combinations of minerals or chromium sulfate.
The "washed lambskin" is an enzyme wash process in which special enzymes are used to help soften the leather. Most of these are aniline leathers which beyond dying only have a limited amount of surface protection. This allows them to breathe more, but also makes them fragile to the elements.
Most garment leathers are a semi-aniline leather which have a little heavier treatment, but make them more resistant to stains, etc. Biggest difference in the semi-aniline is that other dyes are used besides aniline. (aniline is the type of dye)
Leather should never be placed in a dryer and by the same token, leather furniture should not be placed near fireplaces, radiators, etc. Dried leather loses its oils and becomes stiff and brittle and will crack over time.
Also. Watch the dry-cleaners. Many of them use a heavy chemical process that will strip the leather of their oils. I know almost immediately when I come across a dry-cleaned leather because instead of being soft and silky, the leather has almost a papery feel. Most of the time I come across this with white colored leather garments being sold and the people are trying to remove some of the soiling, but in the process really destroy the leather.
There are several leather specialists nationwide who do fabulous jobs cleaning leathers, and will even go to the point of removing the surface and re-dying faded areas that are very prevalent in older aniline leathers like the Plonge Lambskin used by Jitrois, Chanel and other.