Hi Vishal,
1. I said that it will not affect much the local stresses, but you are talking about primary membrane stress (stress due to pressure).
2. Nozzle neck shall not govern the MAWP of the vessel, hence nozzle can not fail.
3. Most important is, MAWP is determined considering effect of static head and EXTERNAL LOADS (Refer definition of MAWP). Hence MAWP should be such that MAWP + external loads + static head causes the stresses less than or equal to allowable stress.