Will the Blu Electronic Cigarette Cartridges work with a V2 e-cig?

No - V2 is an overpriced KR808D1 threaded model - this threading has a male connection on the battery and female on the cartomizer. Blu is NOT a 510 (and in fact will fry on a 510 charger - reverse polarity) but it has 510 thread which has the female thread on the battery and male connection on the cartomizer (what Blu calls cartridges)

However, a KR808D-1 to 510 adapter would let you use Blu cartomizers on V2 or other KR808D-1 model (like V4L or SmokelessImage Volt). BTW V4L standard cartomizers and Smokeless Image Volt cartomizers will work on V2. The Volt cartomizers are higher quality cartomizers IMO but V4L has more flavors.

Blu Cartridges

Blu Cartomizers

Blu Electronic Cigarette don't Cartridges with V2 e - cig . There are tow types of work . One is electronic and other is non electronic . So electronic cigarette are not equal with cartridges .

Blucig carts will work with anything that has a 510 connection, I believe V2 has a KR808 connection. So you'd need an adapter for the Blucig carts to fit V2 batteries.