The guitar pickups will not work on violin, as the violin has an extreme arch to the fingerboard, so the level between the strings would be off, as they are magnetic pickups. Those pickups suck, though, so you are not missing anything.
If you really want something you can move between your violin and mando, you could use something like
THIS, but I don't recommend this, as they can not be put in the place on the instrument (either one) which will sound best. In a live situation, they are also more prone to feedback.
Fishman (and Baggs too, I am sure) also makes a mando pickup, if you need one for the mando.
All piezo pickups require a preamp of some sort to sound their best. Some models, particularly for guitar, have built in preamps, such as the Highlander (which was the first), the Fishman Matrix, or the D-Tar Timbreline. I have not noticed any of these for the violin or mando, however, so you would need some kind of an external preamp, as the output of piezo pickups is millions of ohms, and guitar amps and mic pres and such are looking for a signal in the thousands of ohms. Using a pickup without a preamp will lead to a very tinny, brittle sound, which is very unpleasant. You could, however, use the same preamp for both the violin and mando, though I would suggest getting different pickups.
The other possibility, if this is only for recording, is running the effects processor from either an aux send (preferable, for me), or as an insert on the channel. This way, you get the sonic advantages of the mic, and if you use an aux send you can mix the dry signal with the effected signal to best effect.
By way of full disclosure, I deal both Fishman and Baggs products (though I sell far more Fishmans than Baggs).
Light
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