OK.
I did a small trial, and can confirm that the Solio works with the Iliad (if you put a car-charger in between to make the connection).
I can't give you any exact numbers, but I'd say a fully charged Solio battery will give you about 3/4 chrage for your Iliad (the Iliad has 2 rather strong batteries if I remember correclty). If you leave your Solio somehwere in the open and the sun dis shining, then it should recharge during the day and give you extra-juice for your Iliad in the evenings.
Please be warned however...the Solio needs quite a bit of sunlight to work. I guess this is a problem with all currenty solar equipment...as long as you have direct sunlight it's OK, but as soon as the sky gets overcast you'll be out of luck.
However, since the Solio has a strong battery inside, it can make use of the sun when it's there and store the power for later use so as long as there is enough time to leave it in the sun it should still be useful. Only if it turns into a rainy week...but whi goes hiking on a rainy week anyway...
I'm going to send my Soilo back because for my use (recharging my cellphone when on the train for example) it just does not work well enough in "Half-Light" situations, but if you're an outdoors person then I don't see any reason not to use it.
Using the Car-Charger as go-between for the Iliad might not look pretty, but it gets the job done, and in the end that's what counts.