I just rooted my old 7" Innovatek Innosoul with ICS 4.0.3 and the same specs as yours with the new towelroot rooter (towelroot.com), mostly just to see if I could.
It worked like a charm. In fact, it was easier and smoother than rooting my Asus MemoPad ME301T!
I also installed app mover, app2sd, Supersu and Titanium Backup Pro.
I was able to delete unwanted/unneeded apps and transfer a lot of apps to the SD card freeing up space on the rom.
I also changed the keyboard response to 100.
The tablet is now humming right along (as well as it can with it's limited hardware). There is no keyboard lag at all anymore, apps open and close very quickly, no lag when turning pages while reading books and no Candy Crush game lag!
I am still on the lookout for a generic upgrade from 4.0.3, but the tablet is running smoothly and doing everything I want it to do quite well. I would be happy to leave it just the way it is at this point.