No it will not work. I think this may be tough with a locked bootloader. Chainfire supports CF Autoroot but I believe he is away for the next few weeks. Not sure if he will be able to get it working on the Verizon LTE version but right now, there is no way to root that.
Also, as far as performance, there is really no difference from what I have read. If anything, the 905 *may* be slower due to LTE. What I can say is that the Snapdragon processor will charge faster than the Exynos in the P900.
If you REALLY need root, return the 905V and get a 900. I just tether mine to my HTC one when away from home or a hot spot. You'll also save more than 100 bucks. Verizon is making it very difficult to root with their locked bootloaders and I don't expect these will be in high demand so support from the Dev's may be slim.
Just my .02
I think we will be seeing TWRP support for the P900 in the next day or so. That should help open the door to custom rom's but I expect they are still a month or more away at this point.