As a general rule of thumb, it's generally taken that one should be concerned about conductive objects in an antenna's near field if they are greater than a quarter wavelength in size. If the are not just under but well under then they're probably not a concern. A long threaded rod very well could cause problems. BBs, if they are reasonably well isolated from one another by the epoxy, are probably not.
Which are you concerned about, the GPS signal or the signal you're transmitting? GPS uses three carriers, all within the L-band region, with wavelengths of about 19 cm, 24.5 cm, and 25.5 cm. The one link IO found does not state whether you need to receive all three or just one (or two out of three, but I doubt that) for a fix. So, the quarter-wave size is from a bit under 5 cm to a bit over 6. So BBs might be an issue, but I'd still bet not.
As for your transmission, I don't know the wavelengths involved.
I repeat others: test it.
Aesthetically, I like the idea of an external antenna. A stripe down the side that's actually functional just seems cool.