I think one needs to take a longer perspective here.
Defending a place with a Ring means committing one to the place for real I'd suppose (like in the cases of Elrond and Galadriel) as it is not any "instant magic" you can just put into use whenever you wish (like "puff, you're invisible!"). It means also rooting into that place, keeping it there and safeguarding it... and even if Gandalf loved the hobbits why would he have used such an extraordinary gift of the ring to protect the hobbits when there was nothing of interest for anyone there - none even for Gandalf himself until the things stated rolling and he realised the Ring was there - and then it was of course too late to protect Shire as the Nazgūl were already in there as well knowing the same thing...
So any speculation of Narya protecting the Shire should not speak of Bilbo or the master Ring but the decades before it was found... and there I think it would be possible... even if a bit unbelievable asthe Shire's safety can be explained by the remotedness of it and with the guardianship of the rangers more than well...
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Upon the hearth the fire is red
Beneath the roof there is a bed;
But not yet weary are our feet...
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