4340 is not listed as a soft magnetic material in an article on soft magnetic materials printed in the 2nd Vol of ASM International Handbook 9th ed.
From the same source:
"Magnetically soft materials manufactured in large quantities include high-purity iron, low-carbon irons, silicon steels, iron-nickel alloys, iron-cobalt alloys, ferritic iron-chrome alloys, and ferrites."
No it would not. If it were annealed it might not be too bad. You need to remember that in general the mechanisms that result in mechanical hardness also lead to magnetic hardness.
Cr-Mo steels were used as permanent magnets in the 1920's.
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Corrosion never sleeps, but it can be managed.