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I think it would be possible, but you have to bear in mind that it would also pretty much restrict your string choices to steel strings. Synthetic core strings and a lot of the alloys used with violin strings wouldn't pick up well with a standard electric guitar pickup.
Electric guitar pickups are also a bit long for a violin's string spread. But it would probably work, just maybe be a bit clumsy to bow around unless it was a fairly thin guitar pickup. Almost the only place you could mount it without modifying the violin that I can think of is between the bridge and the fingerboard. If you padded the back of the pickup and came up with some sort of clip to hook it into the F-holes or to the C-bouts, I think it could be done.
Might also want to look for a fairly thin pickup that has adjustable pole pieces so they could be adjusted up to be nearer the strings.
But yeah, logically it *could* work.
"This young wine may have a lot of tannins now, but in 5 or 10 years it is going to be spectacular, despite the fact that right now it tastes like crude oil. You know this is how it is supposed to taste at this stage of development." ~ Itzhak Perlman
Reason I ask is that I have a bunch of old pickups from old guitars that are just going to waste right now and was thinking maybe if I did it right I could strip the copper off and mate the pickup shorter and modify it to fit the violin. And I didn't spent much on my violin so I wouldn't be afraid to modify the instrument in any way. But I suppose your right with the steel core strings. But aren't the synthetic strings wrapped with something or are they 100% synthetic material?