I think the answer is:
"Not with out modification."
Link Removed
Considering it's installed with passive pickups at the moment (stock) and from what I can find on the Squire VM Jazz body, the area under the cover does NOT have enough room for the battery (as it was never installed stock) and pots to fit without modifications. If you have some pictures and measurements of your specific body cavity, we might be able to give a more definitive answer, but I'm assuming you would have some heavy body mods required to make it all fit.
While the J model pickups will drop right in, you may need to invest in the rheostat kit as well since your passive pots resistances are not correct for the active EMG pickups. A lot to consider. Worse comes to worse, most good shops will give you a free estimate if you tell them what your trying to do and promise them the business. Even if they charge you 25 bucks for an analysis, may be better than spending money on parts and running into hick-ups along the way.
I'm an electrical engineer and I still defaulted to a shop for my current project to eliminate self-induced problems due to my lack of specific model knowledge!
Just my two cents though!
I removed my EMG's from my PJ fretless and once I installed a Dimarzio Model J at the bridge and it was like a whole universe opened up.
