No, placing them at the eyepiece does not do much to shorten the light path of the BV. Yes, you would probably have to rack out a bit to reach focus, but most Barlows do not require that much out focus.
To work, the focal extender has to be placed in front of the BV so that it lengths the light cone by the distance though the binoviewer, and this is typically 100mm or more.
And of course once you do this, you wind up with a higher power.
I think the Denk and Earthwin systems have it right. By putting the Barlow far ahead of the binoviewer (130mm or more with a 2" diagonal and as much as 100mm with the Newtonian extender) you can limit the amount of amplification, and when you use this kind of system, it allows you to re-capture some of the lost true field by using the reducer arm.
My standard advice for many years now (which I know offends some people, but it is nothing personal, just advice) is to get a Denk or Earthwin type system with a power switch. These will reach focus in juts about any kind of scope and give a wider true field than is often possible with any other approach. And, you get three powers to boot. By the time you add up the costs of all the additional eyepieces and other OCAs, the price will not seem all that high, and the raw utility of being able to change mangications without changing eyepieces has to be experienced to be appreciated.
The Linear Binoviewer though solves the problem of making one binoviewer work with many scopes, and while the aperture is small, you can probably still get wider fields than you could get using many other binoviewers, even if they have big prisms. It takes about 2.3x to 2.6x of Barlow to offset the light path of a binoviewer. If you start with a 27mm aperture, you get smaller than the aperture of the Orion pretty quickly if you have to use 2x or more to reach focus.
I have my doubt that Orion will sell many of these at the price they advertise, but at $300, I would probably buy one if the optical quality and performance was on par with other BVs.