Is this "..." able to be linkable to the Full view?

Not by configuration.

A.) Create a custom field output template (docs):

YourJoomla ▸ components ▸ com_cobalt ▸ fields ▸ textarea ▸ tmpl ▸ output ▸ yourdefault.php

Rough logic:
The "..." is the default indicator. You can't remove it in backend, except for a "blank" space character. So, you might keep the 3 dots or change it to your own placeholder i.e. [READMORE]. In your custom output template find and replace the "[READMORE] or ..." with the current Record-URL + your own "Indicator". Maybe the language text constant for "Read More"!?

HeadsUp:
The initial textarea content is a paragraph, thus your "..." link might break onto the next line. Then you might have to add a proper SPAN tag and CSS class beforehand... that would allow to adjust the floating/positioning.

B.) Not recommended, but possible as well:
A complete field override in your site templates HTML folder. The indicator is added in the field's main PHP file textarea.php. Look out for seemore parameter around line# 88)

BTW, Text field and HTML field have parameters for ReadMore-button. Including the link functionality. Are those fields an option for you? Little drawback: If you don't want a default bootstrap button-style, you would have to create some CSS rules to remove that visual appearance. (Related topic with sample sceenshot)

Thanks for the detailed steps.