The word you're looking for is "script". And, no.
One has to make a better argument for the external link symbol getting a codepoint assignment. TFA, for example, makes an argument based on emojis -- certainly that's strong enough to blunt the UTC's rejection rationale, but perhaps not enough to win approval outright.
Addressing all the arguments used in the rejection is important, of course. The fact that currently images are used is hardly dispositive: that's business as usual for missing Unicode assignments!!
But there are probably stronger arguments for rejection than adoption than the UTC made that it could make the next time this comes up.
The best argument for rejection that I can think of has to do with layering. An external link character isn't very useful without the actual external link, but the link belongs a layer up: not in the text, but in the markup. Well, if the link belongs a layer up, why not also the symbol? Alternatively, more markup can move into Unicode. There has been and will continue to be some pressure to move more semantics from markup to text, but it's probably best to resist that pressure.
On the other hand, a solid argument for adoption may involve text rendering of HTML. Think of lynx/elinks and other such browsers, which can't use images. An external link character could prove useful in distinguishing the rendering of linked text from, say, underlined non-linked text.
I'm surprised these arguments didn't come up. Or maybe they did -- I've not gone down the rabbit hole on this one, and probably I won't.