Emphatically NO! Those sprouts are poisonous, and the poison will have spread throughout the potato itself. No amount of cooking will remove that poison.
You might survive eating them, but on the other hand you might not. It depends on just how much of the poisons you ingest. Why take the risk, and especially why feed them to your vulnerable children (if you have any)?
You have to be very, very careful with potatoes. Here's a list of some of the components of a potato - the nasty ones increase dramatically in quantity and potency when a potato is green, or is sprouting. There is absolutely NO POINT in removing the green bits or the sprouts - in fact, keeping the rest is more dangerous than eating the bits you've removed!
potassium, calcium, magnesium, phosphorus, sulphur, iron, copper, manganese, zinc, molybdenum, cobalt, nickel, chromium, fluorine, selenium, silicon, rubidium, aluminium, boron, bromine, mercury, arsenic, cadmium and lead. While some of these minerals are toxic in large amounts, they are essential in minute amounts to the human body.
Do yourself a favour and plant the sprouting potatoes instead - that way you'll be much safer, plus you'll get a whole lot of new potatoes before too long.