I'd say no. Plastic nut, plastic saddle, strings shouldn't get that magnetized...Just make sure your humbucker is properly grounded and soldered to the back of your volume pot, the ground from that is properly soldered to the correct lug on the jack (the one that goes to the center ring), you use a properly shielded guitar cable, and your amp is properly grounded.
You might consider putting some proper shielding, either paint, foil or tape, inside the box around the humbucker.
Ground the strings if you can, particulalrly if you are using a singlecoil pickup which may be more prone to hum. Also if you are likely to be using it onstage where there will be lots of other electricl equipment lights etc., it can be very noticeable when that hum is amplified thru an amp and then through the PA.
You'll probably notice the reduction in hum when you touch the strings if it's all properly earthed.