Explicitly modify your mint function with whenNotPaused?

I used the contracts wizard and made sure Pausable was enabled. One override that added was:

function _beforeTokenTransfer(
        address from,
        address to,
        uint256 tokenId
) internal override whenNotPaused {
        super._beforeTokenTransfer(from, to, tokenId);

So this means that ANY transfer cannot proceed if the contract is paused right? Does that include calls to _safeMint()? I have a custom minting function that looks something like:

function myCustomMint(uint256 _mintAmount) public payable nonReentrant {
    // some require statements
    for (uint256 i; i < _mintAmount; i++) {
        uint256 tokenId = _tokenIdCounter.current();
        _safeMint(msg.sender, tokenId);

If my contract is paused, I don't want minting to be enabled. Do I explicitly modify the function signature of myCustomMint() with whenNotPaused? Or does the _beforeTokenTransfer override with the modifier take care of that?

Also, using Pausable, if I want the contract to be paused by default when it's deployed, do I just call _pause(); in the constructor body?

It only overrides the token transfer and not the mint function