Maybe but I'd take a room that you can have a normal conversation in any day over an anechoic environment just to shoot better sounding videos
Why not put up temporary panels out of the camera's view? Studios use goboes for blocking sound all the time- it doesn't need to be anechoic but it doesn't need to be perfect for listening to music or watching a movie since that's not what you're doing at the time, either. The partitions used for office cubicles would be perfect and I would thing you have a place that sells them near you. A lot of voice-over work is done in small rooms that are acoustically dead, or they use something like this-
http://www.dv247.com/assets/products/200177_l.jpg
Parts Express sells one and it's not terribly expensive- it would be great for the videos that you narrate, off-camera. For the others, you just need to re-create the effect of a screen- If you only place the panels behind the camera, it should improve the sound.
If you decide to build some kind of booth for making the videos, you could wear in-ear monitors and add a bit of reverb to the monitor send, so you don't hear yourself without any ambience- having been in an anechoic chamber, I completely understand not wanting to record in one.