No, no.

The English bone china has a clear glaze over the painted patterns.  Even solid white has the covering.  When a dishwasher cycle is run, the water is usually very hot.  That means that the glaze will heat at a different rate than the porcelain itself.  The expansion of the clay will often create a webbing of lines on the surface of the glaze. That is crazing.  

Crazing is the start of damage.  Tea can seep into the tiny cracks and turn brown.  They can color the bone china underneath it.  

The picture shows the inside of a teapot.  Someone poured boiling water into the pot and unwittingly created crazing.  It was still used for years and the darkness resulted.  

Some think that using boiling water is the best way to brew tea.  We have been told to boil the water and then let it sit a short time to slightly cool.  Then pour it into the pot or cup.

Some dishwashers do have a fine china setting.  Use at your own risk.  Our previous unit worked very well.  After Thanksgiving dinner, our Wedgwood dishes were placed there and came out sparkling clean without any damage. However we have heard of terrible results from others.  It is not a question of the china maker, it is the temperature of the water.

Hope this helps you to protect your fine china.