For the vast majority of her existence – No.
Susan Storm was largely the token girl[*] on the Fantastic Four team, a good princess-figure in semi-constant need of rescue despite her quite formidable abilities. Indeed, despite the vast number of comely intelligent women in the Marvel Universe, she was fought over fairly constantly by several of the FF’s male antagonists Doctor Doom, Namor, and even occasionally the Mole Man and other 2nd-tier garbage. Perhaps if she had a catch phrase back then, it would’ve been “Save me, Reed!”
(Nothing will save her from this spanking, though – Photo courtesy http://www.flickr.com/photos/gru…)
Starting in the late 90s/early aughts, however, she has been known to throw the occasional bad pun, especially if it relates to a general “women not being invisible anymore” theme. This was also reflected in various costume changes, which were (ironically?) much more revealing than in her earlier incarnations…
(She’s also awesome to cosplay – you don’t even need to show up to the con – photo courtesy http://www.flickr.com/photos/vic…)
Digging through back issues, and a few pizza-stained comic geek friends[†], though, the best I can come up is the following: “The Female of the species is more deadly than the male.”
(Er, Rudyard Kipling was not… visibly a woman, so it makes sense… Photo courtesy of ancient history)
In summary, it’s kinda pulling at straws to come up with a real catchphrase for Sue Storm. And honestly, comics in general are kinda over catchphrases, so I’m not sure we’ll see a good one arise in the future. Still, the FF has almost always been written and drawn by men, and 3/4ths of the team are guys. Perhaps, with a woman’s touch?[ª]
[* as referred to in the question, her original “code name” was Invisible Girl, not Invisible Woman. Get with the times, Stan!]
[† thanks to Robert McCarthy (howcomics.com), especially, for the much needed assist here and there]
[ª Just, please, not this woman: http://barbara.guanabee.com/2011… ]
This answer originally appeared on Quora: Did the Invisible Woman (Invisible Girl) have a catch phrase?