Yep, it will be noticeable. It's one of those things that becomes clear once you set the tire up there.

http://i645.photobucket.com/albums/uu176/lakeroadster/Generic/sparetire_zpsdb7f06a5.png

My '65: http://i645.photobucket.com/albums/...1530103882008S600x600Q85_zps7ef52950.jpg

Interesting article related to fender mount spares; http://oldchevytrucks.net/Articles/1953-1955-Side-Mount-Spare.php

As stated in the article:

The indention on the 1/2 ton left fender was made no larger than necessary to allow for the mounting of the 6.00 x 16" original tire. This spacing is so close that the current replacement 6.50 x 16" replacement tire will sometimes not fit without touching either the cab or fender indention. This contact of the tire against the metal body and fender is not acceptable. The rubbing of a larger tire against the body or fender results in a squeaking noise and finally will wear through the paint. To prevent this, using a 6.00x16 tire may be necessary.

Been there, done that, as they say thumbs_up