In the strictest terms, yes. For example, Hydroxyurea decreases cell production in the bone marrow and can rapidly decrease a population of white cells called myeloid cells in the case of leukemia where the count can exceed 100,000. This is to prevent leukostasis which is where the cancerous cells thicken the blood and cause it to sludge causing respiratory failure or stroke.

The answer is no. “Blood thinner” is somewhat of a misnomer as it does not change the viscosity or concentration of any component of the blood, but prevents the coagulation cascade at some point depending on the agent used. Beta blockers do reduce cardiac output, but not close to any degree that would compromise flow to an organ system like the GI tract. Not to mention that the stomach, although vascular like you mentioned, does not really perform a lot of absorption of nutrients. This occurs mostly in the small intestine where the blood supply is essential to take nutrients to the portal system.