No. Removing blood leaves an individual in a slightly weakened state. The body does produce new blood to replace that which has been lost, but the 'quality' of the new blood is not better than the old. If too much blood is withdrawn, it can lead to a fatality. This was, however, one of the reasons used to support the ancient medical practice of bleeding a patient. Any 'poisons' in the blood, which were believed to be the cause of many illnesses, could be removed by bleeding the patient. Bleeding a patient, however, tended to leave the individual in a weaker condition, with an increased risk of infection from the bleeding process - an infection could be introduced by contaminated instruments or by contamination of the exposed wound. Medical practitioners, up to about the mid-19th century, had very little idea how the body worked and, therefore, maintained practices that were dangerously wrong. They knew which organs were present and where they were located in the body - the result of millenia of dissections - but had little idea what they did or how they worked. It was believed, for example, that the veins carried blood to the body and that the blood dissipated into the tissue at the end of the trip. The blood itself was manufactured in the liver. The arteries delivered an individual's spritual essence from the heart to the extremities in the same way. Any blood in the arteries, therefore, was the sign of a serious medical condition and bleeding was used to remove arterial blood. This belief stemmed from ignorance concerning the circulatory system and incorrect observations of dissected corpses. Most of the blood drains from the arteries after death and pools in the veins, so it is normal for a corpse to have little or no blood in the arteries. Bleeding patients was the normal method of treating many medical conditions, a process that often resulted in the patient's death. Bleeding a person weakens them, which can make a condition worse by reducing the patient's strength and the ability of the body to fight the disease. There are very few medical conditions that can be helped by bleeding a patient. It has a great potential to be a very dangerous practice. The healthier a patient is, the better their immune system operates and the better the chance of recovery.

Good answer already given. Just to add a few bits of info, in response to the loss of blood cells, specifically the erythrocytes (red cells) that carry the oxygen, a hormone called erythropoetin is increased in production form the kidneys which stimulates bone marrow to increase it's red cell production. Notice I said increase, not start. This is because the total lifespan for any red blood cell is 120 days. Past this (or sometimes beforehand) the cells lyses (disintegrates) and dies. Therefore, red cell production is in constant motion and erythropoetin levels (should) be contsantly present at low levels. This is similar to most body systems, as there is little black and white, on/off states but usually systems are in a state of equilibrium between the on anf off forces. So yes, a greater proportion of your blood a few days after donation is newer, but then your blood never gets "too old" anyway, and as mentioned before, until the cells have been replaced (the actual plasma - the liquid part of the blood- is compensated for almost immediately from other body fluid compartments), the body is actually in a slightly weakened state anyway. If you have ever donated blood you will know this feels like you are not quite 100%, and some susceptible people feel faint or even sick. lets face it, if you cut yourself on some glass and lost a pint of blood, you wouldn't exactly feel better would you?

Consider it an oil change! Look at research involving men and women in regards to heart disease/heart attacks. Women menstrate monthly, men don't. Why do males tend to have a higher heart disease/attack rate than women? The answer is simple, too high of a concentration of iron in ones body. If you donate blood, some of that iron is removed. Look it up for yourself if you dont believe me. The answers are there (WEBMD).