But, fans in that configuration definitely cannot remove 350W of heat. GPUs over a certain threshold need 3-slot widths and giant triple fans in order to stay cool.
Well in theory it certainly can. It is important to not make that claim because it is just easy for BFL to refute. Case in point, the 7990 is 375W TDP and it is a "reference" dual slot design using a similar "squirell cage" blower as their photoshop card. So it is "possible" to have a SHA-2 ASIC which dissipates 350W within the dimensions of a high end 2 slot GPU form factor.
As a practical matter
I doubt BFL will be able to deliver on time, on spec, and on wattage. Everything would need to be perfect from the logistics, to the claimed performance per watt gains to the thermal specs to the fabrication. It is running so close to the limit of what is possible that any failure would almost certainly result in costly delays. Lets put this into perspective, AMD pushed back the launch date of the HD 7990 twice for over six months because they (with decades of GPU design and cooling experience) were running into power/thermal issues.
Simple version: 350W in that form factor is possible but it is close the redline. Worse the specs are based on simulated chips (which for BFL have been horribly wrong in the past). If it uses more power you can't simply go bigger because they decided to use a specific form factor.
A smaller issue is that lets say for the sake of argument they can delivery on time, on spec, and on wattage. Despite the compact dimensions of the card there are going to be real limits on what one system can do. As an experiment if someone wants to plan their future 4U BFL hashing rig
Thermal Testing Load
1x BFL card (350W) ~= 2x7870 (350W)
2x BFL cards (700W) ~= 3x7970s (750W)
3x BFL cards (1050W) ~= 4x7970s (1000W)
4x BFL cards (1500W) ~=6x7970s (1500W)
Take a 4U case (or full tower and seal any top/side/bottom vents. Drop the cards in and try to cool the rig inside a sealed case only using the cards fans plus front intake fans. It isn't going to happen. There is a reason that people starting using extenders and open frame rigs ("ghetto miners"). Trying to remove 1KW or more heat from a closed case is a challenge. The high energy density of GPU cards (x watts isn't evenly distributed across the case area but is instead concentrated in the GPUs) make it very difficult even with high output fans. So you get all the cost/complexity of the GPU form factor while not really gaining higher GH/u (thats GH per rack unit) density.
Still I am sure BFL will lock down $1M in orders or upgrades within a day and that was the point. That will improve their cashflow situation and is enough people upgrade (and delay their delivery till "December") they may even make their backorder promise.