You got me curious, so I did a quick test. I grabbed one of my bench mules, which I use for testing pickups. It's 35" scale, with Chromes on it, up to standard pitch. I held a new 3/8" dia x 1" long A5 rod magnet near a string, right after the heel of the neck, moving it carefully closer to the string, while watching the movement of the string in relation to a fixed line. A 3/8" x 1" A5 is a big honkin' magnet, roughly 4 times the field strength power of a 1/4" magnet (like a Quarter Pounder) and roughly 8 times the power of factory Fender-style pickup magnet.
What I saw was this: With the magnet 1/8" (0.125") or more away from the string, I couldn't see any movement at all of the string. It was 0.001" or less. It didn't matter which gauge, which string. As I moved the magnet under 0.100" away, I could begin to see a little bit of movement, a few thousandths. When I got the gap down to about 0.050", the string would snap over and stick to the magnet.
So:
Yes, Chromes are not the most magnetic strings; steel rounds would be somewhat more magnetic.
But this was a really powerful magnet!
A gap of 0.100" between the magnet and the string at the 24th fret is not really even playable. Any plucking at all, and the string would stick to the magnet.
My conclusion from this is that any normal pickup would have to be unreasonably close to the strings to cause a few thousandth's of an inch of deflection from the magnet's pull.
A related observation about magnets vs strings: The conventional wisdom is that installing pickups with big magnets (like Quarter Pounders) will kill the sustain, because the powerful magnets will slow the strings down quicker. That's what everyone says. But, I can pluck the string on my test mule and listen to its decay, unplugged and unamplified. Pluck it again, and listen to the decay while holding the big magnet next to the string at the 24th fret, moving it as close as possible to the string without sticking to it. I tried, but I can't make the decay faster. And that's with the big honkin' 3/8" magnet held really close. So, how is a measly little Quarter Pounder slowing the string down, when it's normally further away than that?
I can answer that: The bigger magnets put a larger pulse on the beginning of the note- an exaggerated attack curve shape- before settling into the extended ring of the note. The overall volume (level) is louder, so you turn the level down to compensate. And your perception is that the sustain has dropped off. It's actually still there; you've adjusted in response to the big opening pulse.