The answer is yes and no

For the example you asked about (the connection to the base) there is a solution. Instead of having your index.js like this:

var dbMotor = require('my-sql'); // o require('pg-promise-strict'); 
var config = require('./config.json');
var dbOpen = dbMotor.connect(config.parametrosDb);

var app = require('express')();

app.get('/data', function(req, res){
   dbOpen.query("SELECT ALL ... ", function(err, data){
      res.end(data);
   });
});

you can have a database wrapper that only wraps that part:

var dbMotor = require('my-sql'); // o require('pg-promise-strict'); 
var config;
var dbOpen;

var app = require('express')();

function start(){
  config = require('./config.json');
  dbOpen = dbMotor.connect(config.parametrosDb);
}

start(); // lee todo al inciar el servidor

app.get('/reset', function(req, res){
  start(); // vuelve a leer todo al resetear
  res.end("reset ok at "+new Date());
});

app.get('/data', function(req, res){
  dbOpen.query("SELECT ALL ... ", function(err, data){
    res.end(data);
  });
});

Response analysis

1. It is a simplification (many things are missing, the listen, closing the database if it is going to be reopened, etc)
2. The advantage is that you do not have to cut the execution of thenode index.js
3. The important thing to observe is that yes or yes it is necessary to execute again, it startis necessary to see how much of the 4 or 5 seconds are taken by tasks that must be done again
4. In this simplification you have to call /resetfrom the browser, you can choose other triggers, for example one watchFilethat is watching if there were modifications in the configuration file.
5. Another alternative is to have one startfor each type of thing, one for the database, another to read templates from disk, another to change ports, etc.

conclusion

There is no magic solution , everything has to be tested and programmed, someone pays the cost , the programmer programming, the programmer waiting for it to start on each reboot, the user with low performance (of something that is constantly checking if it has changed) , the user with the probability that something has an error.

install forever

sudo npm install forever --global

and then start your app (in debug mode) with:

forever -f -w index.js

then if you make any changes in your index.js you will have an output like this

error: restarting script because change changed
error: Forever detected script was killed by signal: SIGKILL
error: Script restart attempt #1

The -w flag tells node to watch for a change in the index.js file and to restart, it interprets it as an error but it isn't.