Not necessarily,
I'll explain it a little easier:
Inside your game there is a list of palettes an Overworld can use.
This list is about ~ 18 palettes long (at least in firered)
NSE can set which palette an OW can use, by setting a number that references the list (ex 0,1,A)
It does this via "Change Palette"
The list is a certain length long, and is sandwiched in between other data.
This makes adding new OW palettes (ex. beyond the default 18) a technical process.
Now your example of "if I want a OW to have a new palette, that doesn't effect another".
For you to do this you have to either make the table longer and add new palettes, or edit a default palette.
For example, in firered, OW palette 0xB is junk left over from pokemon Ruby.
This makes it a perfect palette to edit to your needs.
You could change palette 0xB 's colors to whatever you want.
(Note palette 0xC is the palette for the OW's (0xB) reflection in water)
To reiterate;
Either make due with the palettes you have,
Use an unused or junk palette, that you can then edit,
or Re-point the entire table to make an entire new list of palettes.
The top 2 can easily be done in NSE, while re-pointing the palette table,
requires some extensive HEX knowledge and is something I would only recommended an really advanced hacker do...