Yes, if you wish to hide this option from your customers during the multiple shipping address checkout process, follow these steps:

First, turn on the option to display the “Ship Another” button instead of the faded out new line option.

Next, add this code somewhere in your theme css files, such as at the bottom of your theme.css.liquid file:

.gs_add-shipping-address {
display:none!important;
}

The result should look like this:

Tim Rokeby-Thomas