In brief: Not exactly. Blood actually doesn't get thinned.  what we call blood thinners are agents that decrease the ability of the blood to clot, usually used in people whose blood clots excessively.
Taking B-complex vitamins, which include vitamin B12, can cause urine to have a bright yellow or even orange color, but check with your doctor to be sure that's what is going on in your case. B vitamins are water-soluble vitamins, which means that what your body doesn't use is excreted in your urine. Riboflavin (vitamin B2) is especially likely to cause this color change in urine. Several medications can also turn urine a bright yellow or orange color. Changes in urine color may also signal certain health problems.
The bright yellow, or neon yellow urine is just due to your body excreting excess B2 or Riboflavin. Too many B2 has no negative side effects, unless you count bright pee to be a negative side effect o_O.