Will I get into mechanical engineering in NIT Goa with a 40k rank in the JEE Main?

No, it is not possible to get admission to the mechanical engineering branch of NIT Puducherry with a rank of 40k, through another state quota. According to the 2020 cutoff trend, the closing cutoff of Mechanical Engineering for general category students was 31725. 

So, your chance of getting admission with a rank of 40k through another state quota is pretty slim.