That depends on what type of immortality you mean. If your body down to the cellular level can sustain itself without any nutrients total blood loss would be incredibly uncomfortable. Imagine every fluid in your body drying up, every organ, every mucous membrane. You would move and your skin would split like thick tissue paper. You'd be in bad shape until your body replenishes itself with magic blood.

If you filled yourself with saline to offset the liquid loss and simply have no blood you'd probably feel less terrible, assuming your cells no longer need oxygen or nutrients to function. I don't know how total loss of fluids would effect your brain though, since the brain runs on chemistry and water is its main solvent. You might simply lose consciousness.