No, Not ever.
Playstation brand has always pushed innovation in hardware and has always tried to bring the most unique and varied New IP's to their playstation consoles. Add to that that prices of games are reduced in a timely manner.
Nintendo has lacked in these 2 aries for many many years now.
This kind of merger would hold Sony back and drive gaming into a stale ( same old same old ) routine.
Sorry, but no way.
Let me correct that for you:
The PlayStation brand has always pushed technical specifications in hardware and has always tried to bring the most new IPs to their consoles.
Nintendo has always pushed hardware innovation and has always tried to bring the most of their existing IPs to their consoles.
But yeah, pretty different philosophies.
Naughty Dog's hardware prowess, Nintendo EAD's taste for gameplay...
Sucker Punch's open world mechanics (ok, ok, it's just awesome parkour and quick travel )+Zelda team
Evolution Studios making F-Zero
Japan Studio+Retro Studios...
..................let me dream.